Nonlinear Dynamics
The study of systems which respond disproportionately (nonlinearly) to initial conditions or perturbing stimuli. Nonlinear systems may exhibit "chaos" which is classically characterized as sensitive dependence on initial conditions. Chaotic systems, while distinguished from more ordered periodic systems, are not random. When their behavior over time is appropriately displayed (in "phase space"), constraints are evident which are described by "strange attractors". Phase space representations of chaotic systems, or strange attractors, usually reveal fractal (FRACTALS) self-similarity across time scales. Natural, including biological, systems often display nonlinear dynamics and chaos.
Fractals
Patterns (real or mathematical) which look similar at different scales, for example the network of airways in the lung which shows similar branching patterns at progressively higher magnifications. Natural fractals are self-similar across a finite range of scales while mathematical fractals are the same across an infinite range. Many natural, including biological, structures are fractal (or fractal-like). Fractals are related to "chaos" (see NONLINEAR DYNAMICS) in that chaotic processes can produce fractal structures in nature, and appropriate representations of chaotic processes usually reveal self-similarity over time.
Models, Cardiovascular
Models, Biological
Models, Neurological
Computer Simulation
Algorithms
Molecular Dynamics Simulation
General practice and the new science emerging from the theories of 'chaos' and complexity. (1/2604)
This paper outlines the general practice world view and introduces the main features of the theories of 'chaos' and complexity. From this, analogies are drawn between general practice and the theories, which suggest a different way of understanding general practice and point to future developments in general practice research. A conceptual and practical link between qualitative and quantitative methods of research is suggested. Methods of combining data about social context with data about individuals and about biomedical factors are discussed. The paper emphasizes the importance of data collected over time and of considering the multiplicative interactions between variables. Finally, the paper suggests that to develop this type of research, general practice many need to reassess systems of categorizing and recording appropriate data. (+info)Inhibitory contributions to spatiotemporal receptive-field structure and direction selectivity in simple cells of cat area 17. (2/2604)
Intracortical inhibition contributes to direction selectivity in primary visual cortex, but how it acts has been unclear. We investigated this problem in simple cells of cat area 17 by taking advantage of the link between spatiotemporal (S-T) receptive-field structure and direction selectivity. Most cells in layer 4 have S-T-oriented receptive fields in which gradients of response timing across the field confer a preferred direction of motion. Linear summation of responses across the receptive field, followed by a static nonlinear amplification, has been shown previously to account for directional tuning in layer 4. We tested the hypotheses that inhibition acts by altering S-T structure or the static nonlinearity or both. Drifting and counterphasing sine wave gratings were used to measure direction selectivity and S-T structure, respectively, in 17 layer 4 simple cells before and during iontophoresis of bicuculline methiodide (BMI), a GABAA antagonist. S-T orientation was quantified from fits to response temporal phase versus stimulus spatial phase data. Bicuculline reduced direction selectivity and S-T orientation in nearly all cells, and reductions in the two measures were well correlated (r = 0.81) and reversible. Using conventional linear predictions based on response phase and amplitude, we found that BMI-induced changes in S-T structure also accounted well for absolute changes in the amplitude and phase of responses to gratings drifting in the preferred and nonpreferred direction. For each cell we also calculated an exponent used to estimate the static nonlinearity. Bicuculline reduced the exponent in most cells, but the changes were not correlated with reductions in direction selectivity. We conclude that GABAA-mediated inhibition influences directional tuning in layer 4 primarily by sculpting S-T receptive-field structure. The source of the inhibition is likely to be other simple cells with certain spatiotemporal relationships to their target. Despite reductions in the two measures, most receptive fields maintained some directional tuning and S-T orientation during BMI. This suggests that their excitatory inputs, arising from the lateral geniculate nucleus and within area 17, are sufficient to create some S-T orientation and that inhibition accentuates it. Finally, BMI also reduced direction selectivity in 8 of 10 simple cells tested in layer 6, but the reductions were not accompanied by systematic changes in S-T structure. This reflects the fact that S-T orientation, as revealed by our first-order measures of the receptive field, is weak there normally. Inhibition likely affects layer 6 cells via more complex, nonlinear interactions. (+info)Estimation of Ki in a competitive enzyme-inhibition model: comparisons among three methods of data analysis. (3/2604)
There are a variety of methods available to calculate the inhibition constant (Ki) that characterizes substrate inhibition by a competitive inhibitor. Linearized versions of the Michaelis-Menten equation (e.g., Lineweaver-Burk, Dixon, etc.) are frequently used, but they often produce substantial errors in parameter estimation. This study was conducted to compare three methods of analysis for the estimation of Ki: simultaneous nonlinear regression (SNLR); nonsimultaneous, nonlinear regression, "KM,app" method; and the Dixon method. Metabolite formation rates were simulated for a competitive inhibition model with random error (corresponding to 10% coefficient of variation). These rates were generated for a control (i.e., no inhibitor) and five inhibitor concentrations with six substrate concentrations per inhibitor and control. The KM/Ki ratios ranged from less than 0.1 to greater than 600. A total of 3 data sets for each of three KM/Ki ratios were generated (i.e., 108 rates/data set per KM/Ki ratio). The mean inhibition and control data were fit simultaneously (SNLR method) using the full competitive enzyme-inhibition equation. In the KM,app method, the mean inhibition and control data were fit separately to the Michaelis-Menten equation. The SNLR approach was the most robust, fastest, and easiest to implement. The KM,app method gave good estimates of Ki but was more time consuming. Both methods gave good recoveries of KM and VMAX values. The Dixon method gave widely ranging and inaccurate estimates of Ki. For reliable estimation of Ki values, the SNLR method is preferred. (+info)Chaos and the transition to ventricular fibrillation: a new approach to antiarrhythmic drug evaluation. (4/2604)
Sudden cardiac death resulting from ventricular fibrillation can be separated into 2 components: initiation of tachycardia and degeneration of tachycardia to fibrillation. Clinical drug studies such as CAST and SWORD demonstrated that focusing exclusively on the first component is inadequate as a therapeutic modality. The hope for developing effective pharmacological therapy rests on a comprehensive understanding of the second component, the transition from tachycardia to fibrillation. We summarize evidence that the transition from tachycardia to fibrillation is a transition to spatiotemporal chaos, with similarities to the quasiperiodic transition to chaos seen in fluid turbulence. In this scenario, chaos results from the interaction of multiple causally independent oscillatory motions. Simulations in 2-dimensional cardiac tissue suggest that the destabilizing oscillatory motions during spiral-wave reentry arise from restitution properties of action potential duration and conduction velocity. The process of spiral-wave breakup in simulated cardiac tissue predicts remarkably well the sequence by which tachycardia degenerates to fibrillation in real cardiac tissue. Modifying action potential duration and conduction velocity restitution characteristics can prevent spiral-wave breakup in simulated cardiac tissue, suggesting that drugs with similar effects in real cardiac tissue may have antifibrillatory efficacy (the Restitution Hypothesis). If valid for the real heart, the Restitution Hypothesis will support a new paradigm for antiarrhythmic drug classification, incorporating an antifibrillatory profile based on effects on cardiac restitution and the traditional antitachycardia profile (classes 1 through 4). (+info)In vitro sensitivity of Plasmodium falciparum to artesunate in Thailand. (5/2604)
Reported are the in vitro susceptibilities of Plasmodium falciparum to artesunate, mefloquine, quinine and chloroquine of 86 isolates and to dihydroartemisinin of 45 isolates collected from areas of high resistance to mefloquine within Thailand near the borders with Myanmar and Cambodia, and from southern Thailand where P. falciparum is generally still sensitive to mefloquine. All the isolates were highly sensitive to artesunate, but the geometric mean IC50S were higher in isolates from the Thai-Myanmar and Thai-Cambodian borders than in those from southern Thailand. The IC50S for mefloquine and artesunate were strongly correlated (Pearson r = 0.605; n = 86; P < 0.00001). As expected, the in vitro sensitivities to dihydroartemisinin and artesunate were similar and strongly correlated (at IC50, Pearson r = 0.695; n = 45; P < 0.00002). The correlation between the activity of mefloquine and artesunate requires further investigation in order to determine the potential for development of cross-resistance in nature. Our results suggest that combination with mefloquine is not the ideal way of protecting the usefulness of artemisinin and its derivatives. A search for more suitable partner drugs to these compounds and careful regulation of their use are necessary in the interest of ensuring their long therapeutic life span. (+info)The relation between body size and normalized small solute clearances in continuous ambulatory peritoneal dialysis. (6/2604)
The normalized peritoneal clearances of small solutes depend on the ratio of their concentration in dialysate and plasma (D/P) and the drain volume (Dv) corrected for some measure of body size such as body water (V) or body surface area (BSA). The clearance formulas (D/P) x (Dv/V) and (D/ P) x (Dv/BSA) can be used to examine why large individuals tend to be underdialyzed. Large people have low normalized drain volumes (Dv/V, Dv/BSA). It is not known whether size affects the D/P ratios. The purpose of this study was to examine the relationship between normalized peritoneal clearances (Kt/Vurea, CCr per 1.73 m2 BSA) and four size indicators (weight, height, V, BSA) in 301 patients on continuous ambulatory peritoneal dialysis (four daily exchanges with 2-L exchange volume) who underwent 613 clearance studies. Highly significant (P < 0.001) nonlinear relationships were found between Kt/Vurea and weight (r2 = 0.371), height (r2 = 0.289), BSA (r2 = 0.436), and V (r2 = 0.527); and between CCr and weight (r2 = 0.178), height (r2 = 0.115), BSA (r2 = 0.199), and V (r2 = 0.151). There were also significant negative correlations between the normalized drain volumes (Dv/V and Dv/BSA) and all four indicators of body size. Raw (not normalized) peritoneal clearances and drain volumes correlated positively with size. However, D/P(urea) or D/P(creatinine) did not vary with any size indicator except for a weak association between D/P(creatinine) and V (r = 0.089, P = 0.028). This association was not confirmed when V was used to stratify subjects into quartiles, and group differences for D/P(creatinine were tested by one-way ANOVA. This study shows that the exclusive cause of the low normalized peritoneal clearances in large subjects on continuous ambulatory peritoneal dialysis is a low normalized drain volume. No evidence was found to indicate that body size influences the D/P ratio of small solutes. The portion of the variance in normalized clearance explained by size varies by size indicator and solute (urea versus creatinine). (+info)Even slight movements disturb analysis of cardiovascular dynamics. (7/2604)
We hypothesized that spontaneous movements (postural adjustments and ideomotion) disturb analysis of heart rate and blood pressure variability and could explain the discrepancy between studies. We measured R-R intervals and systolic blood pressure in nine healthy sitting subjects during three protocols: 1) no movement allowed, 2) movements allowed but not standing, 3) movements and standing allowed. Heart rate and blood pressure were not altered by movements. Movements with or without standing produced a twofold or greater increase of the overall variability of R-R intervals and of the low-frequency components of spectral analysis of heart rate variability. The spectral exponent beta of heart rate variability (1. 123 at rest) was changed by movements (1.364), and the percentage of fractal noise (79% at rest) was increased by standing (91%, coarse-graining spectral analysis). Spontaneous movements could induce a plateau in the correlation dimensions of heart rate variability, but they changed its nonlinear predictability. We suggest that future studies on short-term cardiovascular variability should control spontaneous movements. (+info)Nonlinear, fractal, and spectral analysis of the EEG of lizard, Gallotia galloti. (8/2604)
Electroencephalogram (EEG) from dorsal cortex of lizard Gallotia galloti was analyzed at different temperatures to test the presence of fractal or nonlinear structure during open (OE) and closed eyes (CE), with the aim of comparing these results with those reported for human slow-wave sleep (SWS). Two nonlinear parameters characterizing EEG complexity [correlation dimension (D2)] and predictability [largest Lyapunov exponent (lambda(1))] were calculated, and EEG spectrum and fractal exponent beta were determined via coarse graining spectral analysis. At 25 degrees C, evidence of nonlinear structure was obtained by the surrogate data test, with EEG phase space structure suggesting the presence of deterministic chaos (D2 approximately 6, lambda(1) approximately 1. 5). Both nonlinear parameters were greater in OE than in CE and for the right hemisphere in both situations. At 35 degrees C the evidence of nonlinearity was not conclusive and differences between states disappeared, whereas interhemispheric differences remained for lambda(1). Harmonic power always increased with temperature within the band 8-30 Hz, but only with OE within the band 0.3-7.5 Hz. Qualitative similarities found between lizard and human SWS EEG support the hypothesis that reptilian waking could evolve into mammalian SWS. (+info)"Nonlinear dynamics is a branch of mathematics and physics that deals with the study of complex systems characterized by dynamic behaviors that cannot be described by linear relationships or models."
"Nonlinear dynamics is a branch of mathematics and physics that deals with the study of systems that exhibit nonlinear behavior, where the output is not directly proportional to the input. In the context of medicine, nonlinear dynamics can be used to model complex biological systems such as the human cardiovascular system or the brain, where the interactions between different components can lead to emergent properties and behaviors that are difficult to predict using traditional linear methods. Nonlinear dynamic models can help to understand the underlying mechanisms of these systems, make predictions about their behavior, and develop interventions to improve health outcomes."
While fractals are not a medical term, I understand you are asking for a simplified explanation that could be relevant to medicine, so here it is: Fractals can be described as complex geometric patterns that repeat themselves at different scales, and they have been used in certain medical fields such as imaging and understanding the structure of biological systems, like lungs or blood vessels.
I'm sorry for any confusion, but "fractals" is not a term that has a medical definition. Fractals are mathematical sets that exhibit a repeating pattern that displays at every scale, which means they appear similar at different levels of magnification. They are often used in the field of mathematics and computer graphics, but not typically in medicine.
If you have any medical concerns or questions, I would be happy to try to help answer those for you.
Cardiovascular models are physiologically accurate representations or simulations of the human cardiovascular system, its components, or related processes, which may be physical (e.g., mechanical, flow-based) or computational (e.g., lumped parameter, finite element) in nature, and are used for various purposes such as research, education, medical training, device testing, or surgical planning.
Cardiovascular models are simplified representations or simulations of the human cardiovascular system used in medical research, education, and training. These models can be physical, computational, or mathematical and are designed to replicate various aspects of the heart, blood vessels, and blood flow. They can help researchers study the structure and function of the cardiovascular system, test new treatments and interventions, and train healthcare professionals in diagnostic and therapeutic techniques.
Physical cardiovascular models may include artificial hearts, blood vessels, or circulation systems made from materials such as plastic, rubber, or silicone. These models can be used to study the mechanics of heart valves, the effects of different surgical procedures, or the impact of various medical devices on blood flow.
Computational and mathematical cardiovascular models use algorithms and equations to simulate the behavior of the cardiovascular system. These models may range from simple representations of a single heart chamber to complex simulations of the entire circulatory system. They can be used to study the electrical activity of the heart, the biomechanics of blood flow, or the distribution of drugs in the body.
Overall, cardiovascular models play an essential role in advancing our understanding of the human body and improving patient care.
Biological models are simplified representations or systems that mimic specific biological processes, structures, or organisms, used to understand, predict, or test various aspects of biological phenomena, such as disease progression or drug response, through experimental manipulation and observation.
Biological models, also known as physiological models or organismal models, are simplified representations of biological systems, processes, or mechanisms that are used to understand and explain the underlying principles and relationships. These models can be theoretical (conceptual or mathematical) or physical (such as anatomical models, cell cultures, or animal models). They are widely used in biomedical research to study various phenomena, including disease pathophysiology, drug action, and therapeutic interventions.
Examples of biological models include:
1. Mathematical models: These use mathematical equations and formulas to describe complex biological systems or processes, such as population dynamics, metabolic pathways, or gene regulation networks. They can help predict the behavior of these systems under different conditions and test hypotheses about their underlying mechanisms.
2. Cell cultures: These are collections of cells grown in a controlled environment, typically in a laboratory dish or flask. They can be used to study cellular processes, such as signal transduction, gene expression, or metabolism, and to test the effects of drugs or other treatments on these processes.
3. Animal models: These are living organisms, usually vertebrates like mice, rats, or non-human primates, that are used to study various aspects of human biology and disease. They can provide valuable insights into the pathophysiology of diseases, the mechanisms of drug action, and the safety and efficacy of new therapies.
4. Anatomical models: These are physical representations of biological structures or systems, such as plastic models of organs or tissues, that can be used for educational purposes or to plan surgical procedures. They can also serve as a basis for developing more sophisticated models, such as computer simulations or 3D-printed replicas.
Overall, biological models play a crucial role in advancing our understanding of biology and medicine, helping to identify new targets for therapeutic intervention, develop novel drugs and treatments, and improve human health.
"Neurological models are simplified representations or simulations of the human nervous system, its components, processes, or diseases, which are used to understand, explain, or predict neurological phenomena, often for research, educational, or clinical purposes."
Neurological models are simplified representations or simulations of various aspects of the nervous system, including its structure, function, and processes. These models can be theoretical, computational, or physical and are used to understand, explain, and predict neurological phenomena. They may focus on specific neurological diseases, disorders, or functions, such as memory, learning, or movement. The goal of these models is to provide insights into the complex workings of the nervous system that cannot be easily observed or understood through direct examination alone.
"A Computer Simulation in a medical context is a recreation of a medical scenario, process or system, using computer hardware and software to create a model that can be manipulated, studied and analyzed to enhance understanding, improve predictions, or test new concepts without risk to actual patients."
A computer simulation is a process that involves creating a model of a real-world system or phenomenon on a computer and then using that model to run experiments and make predictions about how the system will behave under different conditions. In the medical field, computer simulations are used for a variety of purposes, including:
1. Training and education: Computer simulations can be used to create realistic virtual environments where medical students and professionals can practice their skills and learn new procedures without risk to actual patients. For example, surgeons may use simulation software to practice complex surgical techniques before performing them on real patients.
2. Research and development: Computer simulations can help medical researchers study the behavior of biological systems at a level of detail that would be difficult or impossible to achieve through experimental methods alone. By creating detailed models of cells, tissues, organs, or even entire organisms, researchers can use simulation software to explore how these systems function and how they respond to different stimuli.
3. Drug discovery and development: Computer simulations are an essential tool in modern drug discovery and development. By modeling the behavior of drugs at a molecular level, researchers can predict how they will interact with their targets in the body and identify potential side effects or toxicities. This information can help guide the design of new drugs and reduce the need for expensive and time-consuming clinical trials.
4. Personalized medicine: Computer simulations can be used to create personalized models of individual patients based on their unique genetic, physiological, and environmental characteristics. These models can then be used to predict how a patient will respond to different treatments and identify the most effective therapy for their specific condition.
Overall, computer simulations are a powerful tool in modern medicine, enabling researchers and clinicians to study complex systems and make predictions about how they will behave under a wide range of conditions. By providing insights into the behavior of biological systems at a level of detail that would be difficult or impossible to achieve through experimental methods alone, computer simulations are helping to advance our understanding of human health and disease.
In the context of medicine, an algorithm refers to a step-by-step procedure or set of rules that healthcare professionals use to diagnose and manage specific medical conditions, often presented in a flowchart format for easy understanding and implementation.
An algorithm is not a medical term, but rather a concept from computer science and mathematics. In the context of medicine, algorithms are often used to describe step-by-step procedures for diagnosing or managing medical conditions. These procedures typically involve a series of rules or decision points that help healthcare professionals make informed decisions about patient care.
For example, an algorithm for diagnosing a particular type of heart disease might involve taking a patient's medical history, performing a physical exam, ordering certain diagnostic tests, and interpreting the results in a specific way. By following this algorithm, healthcare professionals can ensure that they are using a consistent and evidence-based approach to making a diagnosis.
Algorithms can also be used to guide treatment decisions. For instance, an algorithm for managing diabetes might involve setting target blood sugar levels, recommending certain medications or lifestyle changes based on the patient's individual needs, and monitoring the patient's response to treatment over time.
Overall, algorithms are valuable tools in medicine because they help standardize clinical decision-making and ensure that patients receive high-quality care based on the latest scientific evidence.
"Heart rate is the number of times your heart beats per minute, reflecting the cardiovascular system's response to physical activity, emotional stress, illness, or medications."
Heart rate is the number of heartbeats per unit of time, often expressed as beats per minute (bpm). It can vary significantly depending on factors such as age, physical fitness, emotions, and overall health status. A resting heart rate between 60-100 bpm is generally considered normal for adults, but athletes and individuals with high levels of physical fitness may have a resting heart rate below 60 bpm due to their enhanced cardiovascular efficiency. Monitoring heart rate can provide valuable insights into an individual's health status, exercise intensity, and response to various treatments or interventions.
"Molecular Dynamics Simulation is a computational method that simulates the physical movements of atoms and molecules over time, based on mathematical equations describing their motion and interactions, to understand and predict molecular behavior and properties at the atomic level."
Molecular Dynamics (MD) simulation is a computational method used in the field of molecular modeling and molecular physics. It involves simulating the motions and interactions of atoms and molecules over time, based on classical mechanics or quantum mechanics. In MD simulations, the equations of motion for each atom are repeatedly solved, allowing researchers to study the dynamic behavior of molecular systems, such as protein folding, ligand-protein binding, and chemical reactions. These simulations provide valuable insights into the structural and functional properties of biological macromolecules at the atomic level, and have become an essential tool in modern drug discovery and development.
'Population dynamics' in a medical context refers to the study of changes and growth patterns in the size, age structure, and distribution of specific populations (such as disease-carrying vectors or patient groups) over time, which helps inform public health strategies and interventions.
Population dynamics, in the context of public health and epidemiology, refers to the study of the changes in size and structure of a population over time, as well as the factors that contribute to those changes. This can include birth rates, death rates, migration patterns, aging, and other demographic characteristics. Understanding population dynamics is crucial for planning and implementing public health interventions, such as vaccination programs or disease prevention strategies, as they allow researchers and policymakers to identify vulnerable populations, predict future health trends, and evaluate the impact of public health initiatives.
Nonlinear Dynamics (journal)
Nonlinear Dynamics, An International Journal of Nonlinear Dynamics and Chaos in Engineering Systems is a monthly peer-reviewed ... "Nonlinear Dynamics". 2022 Journal Citation Reports. Web of Science (Science ed.). Clarivate Analytics. 2022. Official website v ... or the Russian Journal of Nonlinear Dynamics). The journal is abstracted and indexed in: Chemical Abstracts Service Current ... scientific journal covering all nonlinear dynamic phenomena associated with mechanical, structural, civil, aeronautical, ocean ...
Sparse identification of non-linear dynamics
Sparse identification of nonlinear dynamics (SINDy) is a data-driven algorithm for obtaining dynamical systems from data. Given ... "Inferring biological networks by sparse identification of nonlinear dynamics". arXiv:1605.08368 [math.DS]. (Articles with short ... This procedure relies on the assumption that most physical systems only have a few dominant terms which dictate the dynamics, ... It has been applied to identify the dynamics of fluids, based on proper orthogonal decomposition, as well as other complex ...
Journal of Computational and Nonlinear Dynamics
Nonlinear Dynamics is a quarterly peer-reviewed multidisciplinary scientific journal covering the study of nonlinear dynamics. ... "Journal of Computational and Nonlinear Dynamics". 2017 Journal Citation Reports. Web of Science (Science ed.). Clarivate ... Dynamics (mechanics), English-language journals, Systems science literature, American Society of Mechanical Engineers academic ...
Nonlinear dimensionality reduction
Nonlinear Dynamics. 86 (3): 1493-1534. arXiv:1602.00560. doi:10.1007/s11071-016-2974-z. S2CID 44074026. Gashler, M.; Martinez, ... Nonlinear PCA (NLPCA) uses backpropagation to train a multi-layer perceptron (MLP) to fit to a manifold. Unlike typical MLP ... Like kernel PCA they use a kernel function to form a non linear mapping (in the form of a Gaussian process). However, in the ... Nonlinear dimensionality reduction, also known as manifold learning, refers to various related techniques that aim to project ...
Oleksandr Sharkovsky
Sharkovsky, A. N. (2006-06-01). "Ideal Turbulence". Nonlinear Dynamics. 44 (1): 15-27. doi:10.1007/s11071-006-1931-7. ISSN 1573 ... Sharkovsky, A. N.; Kolyada, S. F.; Sivak, A. G.; Fedorenko, V. V. (1997). Dynamics of One-Dimensional Maps. doi:10.1007/978-94- ... The formation and development of chaotic dynamics are associated with his name. In the scientific literature, you can find such ... Sharkovsky, A.N. (November 2019). "Sharkovsky ordering and combinatorial dynamics" (PDF). Sharkovsky, A.; Romanenko, E.; ...
Lyapunov exponent
Nonlinear Dynamics. 85 (1): 195-201. arXiv:1410.2016. doi:10.1007/s11071-016-2678-4. S2CID 119650438. Miller, R. H. (1964). " ... The use of nonlinear mappings to model the evolution of small displacements from the attractor has been shown to dramatically ... A word of caution: unlike the global exponents, these local exponents are not invariant under a nonlinear change of coordinates ... F Ginelli; P Poggi; A Turchi; H Chaté; R Livi; A Politi (2007). "Characterizing Dynamics with Covariant Lyapunov Vectors" (PDF ...
Lyapunov dimension
Nonlinear Dynamics. 92 (2): 267-285. arXiv:1504.04723. doi:10.1007/s11071-018-4054-z. S2CID 254888463. Douady, A.; Oesterle, J ... Nonlinear Dynamics. 85 (1): 195-201. arXiv:1410.2016. doi:10.1007/s11071-016-2678-4. S2CID 254894000. P. Cvitanovic; R. Artuso ... Eden, A.; Foias, C.; Temam, R. (1991). "Local and global Lyapunov exponents". Journal of Dynamics and Differential Equations. 3 ...
Model order reduction
Nonlinear Dynamics. 41 (1-3): 147-169. CiteSeerX 10.1.1.530.8349. doi:10.1007/s11071-005-2803-2. ISSN 0924-090X. S2CID 17625377 ... Computational fluid dynamics studies often involve models solving the Navier-Stokes equations with a number of degrees of ... Nonlinear manifold methods. The simplified physics approach can be described to be analogous to the traditional mathematical ... Empirical gramians can be computed for linear and nonlinear control systems for purposes of model order reduction, uncertainty ...
Tent map
"On risk and market sentiments driving financial share price dynamics". Nonlinear Dynamics. 111 (17): 16585-16604. doi:10.1007/ ... Nonlinear Dynamics. 87 (1): 127-133. doi:10.1007/s11071-016-3030-8. ISSN 1573-269X. Lampart, Marek; Lampartová, Alžběta; ... In fact, the dynamics will be non-periodic if and only if x 0 {\displaystyle x_{0}} is irrational. This can be seen by noting ... Brock, William A.; Dechert, W. Davis (1991-01-01), "Chapter 40 Non-linear dynamical systems: Instability and chaos in economics ...
Bill Buchanan (computer scientist)
Nonlinear Dynamics. 99 (4): 3065-3087. doi:10.1007/s11071-020-05463-3. ISSN 1573-269X. S2CID 210859204. Khan, Jan Sher; Boulila ...
Hyperion (moon)
Nonlinear Dynamics. 81 (4): 2031. Bibcode:2015NonLD..81.2031J. doi:10.1007/s11071-015-2123-0. S2CID 124747289. Wisdom, J.; ... M. Tarnopolski (Feb 2017). "Influence of a second satellite on the rotational dynamics of an oblate moon". Celestial Mechanics ... M. Tarnopolski (May 2015). "Nonlinear time-series analysis of Hyperion's lightcurves". Astrophysics and Space Science. 357 (2 ...
Tilde
"Comparison of Various Techniques for Modelling Flexible Beams in Multibody Dynamics". Nonlinear Dynamics. 12 (4): 367-397. doi: ...
Nikolay V. Kuznetsov
Conference on Nonlinear Dynamics and Complexity, USA, 2021 Kuznetsov, N.V.; Lobachev, M.Yu.; Yuldashev, M.V.; Yuldashev, R.V.; ... Nonlinear Dynamics. 102 (2): 713-732. doi:10.1007/s11071-020-05856-4. Kuznetsov, N.V.; Leonov, G.A.; Mokaev, T.N.; Prasad, A.; ... Nonlinear Dynamics. 92 (2): 267-285. arXiv:1504.04723. doi:10.1007/s11071-018-4054-z. S2CID 54706479. Dudkowski D.; Jafari S.; ... Nonlinear Dynamics. 111 (6): 5859-5887. doi:10.1007/s11071-022-08078-y. S2CID 255049732. Kuznetsov, Nikolay; Reitmann, Volker ( ...
Leonid Manevitch
... to nonstationary dynamics of nonlinear oscillatory systems; to molecular dynamics and physics of polymers and composite ... He made fundamental contributions to areas of nonlinear dynamics, composite and polymer physics, and asymptotology. Manevitch ... "In memory of Professor Leonid I. Manevitch". Nonlinear Dynamics. 16 (3): 527-528. February 14, 2020. doi:10.20537/nd200309 - ... Kluwer Academic Publishers (2002). Awrejcewicz J., Andrianov I., Manevitch L.: Asymptotic Approaches in Nonlinear Dynamics: New ...
Predictive engineering analytics
... modeling of complex structures with linear and nonlinear components". Nonlinear Dynamics. 47 (1-3): 193-217. doi:10.1007/s11071 ... It is a well-established technology that has been used for many applications, such as structural dynamics, vibro-acoustics, ... ISBN 978-3-642-12597-3. Cibrario, V.; Cugnon, F. (2012). "New Technologies in Driving Dynamics Performance Simulation". Lecture ... Structural Dynamics. 3: 1501-1512. Manzato, Simone; Peeters, Bart; Toso, Alessandro; Van der Auweraer, Herman; Osgood, Richard ...
Functional differential equation
García López, Álvaro (1 September 2020). "On an electrodynamic origin of quantum fluctuations". Nonlinear Dynamics. 102 (1): ... Xu, Changjin; Wu, Yusen (2013). "Dynamics in a Lotka-Volterra Predator-Prey Model with Time-varying Delays". Abstract and ...
Rabinovich-Fabrikant equations
Nonlinear Dynamics. 88 (1): 791-805. arXiv:1511.07765. doi:10.1007/s11071-016-3276-1. S2CID 119303488. Sprott, Julien C. (2003 ... Danca M.-F.; Kuznetsov N.; Chen G. (2017). "Unusual dynamics and hidden attractors of the Rabinovich-Fabrikant system". ... Dynamics of Continuous, Discrete and Impulsive Systems. Series B: Applications & Algorithms. Watam Press. 15: 155-164. hdl: ...
Chua's circuit
and first confirmation of hidden chaos was reported in 2022 at the Theoretical Nonlinear Dynamics Lab at the Institute of Radio ... the dynamics of Chua's circuit can be accurately modeled by means of a system of three nonlinear ordinary differential ... Nonlinear Dynamics. 111 (6): 5859-5887. doi:10.1007/s11071-022-08078-y. S2CID 255049732. Z. Galias, "Positive topological ... The nonlinear resistor is implemented by two linear resistors and two diodes. At the far right is a negative impedance ...
Maor Farid
Nonlinear Dynamics. 92 (4): 1517-1538. arXiv:1703.02017. doi:10.1007/s11071-018-4144-y. S2CID 254894294. Maor Farid, Nissim ... "Response regimes in equivalent mechanical model of strongly nonlinear liquid sloshing". International Journal of Non-Linear ... Maor Farid, Oleg Gendelman (2018). "Response regimes in equivalent mechanical model of moderately nonlinear liquid sloshing". ...
Chaos theory
Dal Forno, Arianna; Merlone, Ugo (2013). "Nonlinear dynamics in work groups with Bion's basic assumptions". Nonlinear Dynamics ... Life Sciences Nonlinear Dynamics Research Group at CSDC, Florence Italy Nonlinear dynamics: how science comprehends chaos, talk ... Nonlinear Dynamics. Models of bifurcation and chaos by Elmer G. Wiens Gleick's Chaos (excerpt) Archived 2007-02-02 at the ... Okulov, A Yu; Oraevskiĭ, A N (1988). "Spatiotemporal dynamics of a wave packet in nonlinear medium and discrete maps". In N.G. ...
Absement
Nonlinear Dynamics, 1-14. Mann, S., Pierce, C., Zheng, B. C., Hernandez, J., Scavuzzo, C., & Mann, C. (2019, November). ... Nonlinear Dynamics. 80 (1-2): 457-489. doi:10.1007/s11071-014-1882-3. S2CID 254891059. for example, a new concept and state ...
Spectral submanifold
"How to compute invariant manifolds and their reduced dynamics in high-dimensional finite element models". Nonlinear Dynamics. ... Nonlinear Dynamics. 86 (3): 1493-1534. arXiv:1602.00560. doi:10.1007/s11071-016-2974-z. S2CID 44074026. Cabré, P.; Fontich, E ... Nonlinear Dynamics. 41 (1-3): 1-15. doi:10.1007/s11071-005-2790-3. S2CID 14728580. Ponsioen, Sten; Pedergnana, Tiemo; Haller, ... and therefore motivates the use of SSMs in nonlinear dimensionality reduction. Consider a nonlinear ordinary differential ...
Falling cat problem
Nonlinear Dynamics. 79 (4): 2237-2250. doi:10.1007/s11071-014-1741-2. S2CID 120984496. Lagrangian Reduction and the Falling Cat ... The dynamics of the falling cat have been explained using the Udwadia-Kalaba equation. The falling cat problem has elicited ... Framed in this way, the dynamics of the falling cat problem is a prototypical example of a nonholonomic system, the study of ... Montgomery, R. (1993). "Gauge Theory of the Falling Cat". In Enos, M.J. (ed.). Dynamics and Control of Mechanical Systems (PDF ...
Brain storm optimization algorithm
Nonlinear Dynamics. 78 (3): 1973-1988. doi:10.1007/s11071-014-1579-7. S2CID 120591309. "Keynote Speakers-ICCEM 2019". ICCEM ...
R. Cengiz Ertekin
Nonlinear Dynamics. 91 (2): 975-994. doi:10.1007/s11071-017-3923-1. S2CID 125174958. Ertekin, R. C; Xia, Dingwu (2014). " ... including nonlinear wave diffraction and refraction(see e.g.), nonlinear wave loads on vertical cylinders (see e.g.), wave ... Kim, J. W.; Bai, K. J.; Ertekin, R. C.; Webster, W. C. (2003). "A Strongly-Nonlinear Model for Water Waves in Water of Variable ... Working under close guidance of his advisors, he was one of the first to use the nonlinear equations (that were introduced just ...
Currency strength
Nonlinear Dynamics. 98 (3): 2349-2364. arXiv:1906.07491. doi:10.1007/s11071-019-05335-5. ISSN 1573-269X. Gill, Tanvir (2020-03- ...
Classical central-force problem
Mahomed FM, Vawda F (2000). "Application of Symmetries to Central Force Problems". Nonlinear Dynamics. 21 (4): 307-315. doi: ... ISBN 0-201-07392-7. Whittaker, E. T. (1937). A Treatise on the Analytical Dynamics of Particles and Rigid Bodies, with an ...
Magd Abdel Wahab
... fracture mechanics and dynamics and vibration of structures. In a paper for nonlinear transient analysis of smart piezoelectric ... Nonlinear Dynamics. 87 (2): 879-894. doi:10.1007/s11071-016-3085-6. S2CID 126015447. Phung-Van, P.; De Lorenzis, L.; Thai, ... "Dynamics and Vibration: An Introduction". Amazon. (Use dmy dates from June 2022, Articles with short description, Short ... Wahab has published over 550 papers and technical reports in Solid Mechanics and Dynamics of Structures. He has been cited over ...
Lorenz system
A detailed derivation may be found, for example, in nonlinear dynamics texts from Hilborn (2000), Appendix C; Bergé, Pomeau & ... Gorman, M.; Widmann, P.J.; Robbins, K.A. (1986). "Nonlinear dynamics of a convection loop: A quantitative comparison of ... Hilborn, Robert C. (2000). Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers (second ed.). Oxford ... Nonlinear Dynamics. 102 (2): 713-732. doi:10.1007/s11071-020-05856-4. Grassberger & Procaccia (1983) Leonov et al. (2016) ...
Abel equation of the first kind
Nonlinear Dynamics. 28: 1-16. doi:10.1023/A:1014925032022. S2CID 117115358.. (Old link: On the Solution of the Unforced Damped ... "Construction of Exact Parametric or Closed Form Solutions of Some Unsolvable Classes of Nonlinear ODEs (Abel's Nonlinear ODEs ... Construction of Exact Parametric or Closed Form Solutions of Some Unsolvable Classes of Nonlinear ODEs (Abel's Nonlinear ODEs ... of the First Kind and Relative Degenerate Equations) Mancas, Stefan C., Rosu, Haret C., Integrable dissipative nonlinear second ...
Nonlinear Dynamics (journal) - Wikipedia
Nonlinear Dynamics, An International Journal of Nonlinear Dynamics and Chaos in Engineering Systems is a monthly peer-reviewed ... "Nonlinear Dynamics". 2022 Journal Citation Reports. Web of Science (Science ed.). Clarivate Analytics. 2022. Official website v ... or the Russian Journal of Nonlinear Dynamics). The journal is abstracted and indexed in: Chemical Abstracts Service Current ... scientific journal covering all nonlinear dynamic phenomena associated with mechanical, structural, civil, aeronautical, ocean ...
Journal of Computational & Nonlinear Dynamics | ASME - ASME
... nonlinear dynamics, ASMEs goal is to provide members a medium for rapid dissemination of original research results in ... nonlinear dynamics. Members pay LESS THAN 15% of the listed price! ... of dynamics associated with nonlinear systems. The broad scope of the journal encompasses all computational and nonlinear ... Journal of Computational and Nonlinear Dynamics. ASME. This Standard was last reviewed and reaffirmed in {{activeProduct. ...
Dynamics of Nonlinear and Dispersion Managed Solitons | NIST
Quraishi, Q. , Cundiff, S. , Boaz, I. and Ablowitz, M. (2005), Dynamics of Nonlinear and Dispersion Managed Solitons, Physical ... www.nist.gov/publications/dynamics-nonlinear-and-dispersion-managed-solitons-0 ... An asymptotic theory for the nonlinear and dispersion managed solitons agrees well with the experimental data. ...
COSIS.net - Schedule - NP6.08 Nonlinear geophysical fluid dynamics
"Nonlinear dynamics and chaos in emerging capital markets" by Vivek...
Studies in Nonlinear Dynamics & Econometrics Volume 9 Issue 1
... issue 1 of the journal Studies in Nonlinear Dynamics & Econometrics was published in 2005. ... The Best Paper in 2019 for Studies in Nonlinear Dynamics and Econometrics, has been awarded to Chang-Jin Kim and Yunmi Kim for ... The Best Paper in 2016 for Studies in Nonlinear Dynamics and Econometrics has been awarded to Mark J. Jensen for his paper: " ... The Best Paper in 2015 for Studies in Nonlinear Dynamics and Econometrics has been awarded to Markus Jochmann and Gary Koop for ...
Long time dynamics of \(2d\) Euler and nonlinear inviscid damping
Model reduction of the tippedisk: a path to the full analysis | Nonlinear Dynamics
Le Saux, C., Leine, R.I., Glocker, C.: Dynamics of a rolling disk in the presence of dry friction. J. Nonlinear Sci. 15(1), 27- ... The qualitative behavior of the nonlinear system can be analyzed, leading to slow-fast dynamics. Since even a freely rotating ... 15). Just because of the vanishing real parts of \(\lambda _3\) and \(\lambda _4\), a stability statement about the nonlinear ... qualitative dynamics are preserved in order to obtain a reduced model that will serve as the basis for a following nonlinear ...
Introduction to Nonlinear Dynamics and Chaos - Amrita Vishwa Vidyapeetham
"Nonlinear Dynamics and Chaos",Reading, Addison-Wesley, 1994.. *Robert C. Hilborn, "Chaos and Nonlinear Dynamics", Second ... Familiarize with nonlinear dynamics concepts for better understanding of physical systems. *Demonstrate analytical and ... Lakshmanan M. and Rajashekhar S., "Nonlinear Dynamics", Springer Verlag, 2003.. *Robert L. Devaney, "An Introduction to Chaotic ... biological and financial systems using nonlinear dynamics tools ... Introduction to Nonlinear Dynamics and Chaos. Course Code. ...
Chaos and Politics: Applications of Nonlinear Dynamics to Socio-Political Issues | Santa Fe Institute
... originally due to Malthus and indicate how the incorporation of nonlinear effects alters dramatically the expected dynamics of ... We discuss the extent to which recent improvements in our understanding of inherently nonlinear phenomena present challenges to ... In particular, we demonstrate that the "deterministic chaos" present in many nonlinear systems can impose fundamental ...
Resources | Dynamics of Nonlinear Systems | Electrical Engineering and Computer Science | MIT OpenCourseWare
Video: Demetrios Papageorgiou, "Nonlinear dynamics of multilayer flows in channels"
Nonlinear dynamics of multilayer flows in channels. Demetrios Papageorgiou, Video: Nonlinear dynamics of multilayer flows in ... Demetrios Papageorgiou, Video: Nonlinear dynamics of multilayer flows in channels. Demetrios Papageorgiou, Nonlinear dynamics ... Nonlinear dynamics of multilayer flows in channels. ...
Center for Nonlinear Dynamics » Publication » Cracks and atoms
Center for Nonlinear Dynamics » Seminar » Professor Daniel Goldman
Nonlinear Dynamics in Biological Systems - OpenWetWare
This course is an introduction to nonlinear dynamics with applications to biology targeted to junior/senior engineering ... Mon Sept 10 - Strogatz Chapter 4, Flow on a Circle, Nonlinear Oscillator, Excitable Cells , Basics of Neuron Physiology ... Fri Sept 15 - finish basics of neuron physiology, return to nonlinear oscillator example of a simple excitable cell ... Fri Sept 21 - chapter 6 non-linear 2D systems, Example Lotka-Volterra problem. Nullclines, eigenvector analysis. ...
CMES | Non-Linear Rigid Body Dynamics: Energy and Momentum Conserving Algorithm
APS -75th Annual Meeting of the Division of Fluid Dynamics
- Event - Nonlinear dynamics of thermoacoustic oscillations in...
Physics 615: Nonlinear Dynamics of Extended Systems - UMD Physics
![Third-order nonlinear optical response and ultrafast dynamics of tetraoxa[22]porphyrin(2.1.2.1)s - Journal of Materials...](data:image/png;base64,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)
Third-order nonlinear optical response and ultrafast dynamics of tetraoxa[22]porphyrin(2.1.2.1)s - Journal of Materials...
Ultrafast dynamics and third-order nonlinear optical studies of tetraoxa[22]porphyrin(2.1.2.1)s are reported using a single ... Third-order nonlinear optical response and ultrafast dynamics of tetraoxa[22]porphyrin(2.1.2.1)s K. Makhal, S. Arora, P. Kaur, ... Third-order nonlinear optical response and ultrafast dynamics of tetraoxa[22]porphyrin(2.1.2.1)s† ... Ultrafast dynamics and third-order nonlinear optical studies of tetraoxa[22]porphyrin(2.1.2.1)s are reported using a single ...
Fully-Coupled Nonlinear 3-D Time-Domain Simulation of Drilling Dysfunctions Using a Multi-Body Dynamics Approach | SPE/IADC...
Fully-Coupled Nonlinear 3-D Time-Domain Simulation of Drilling Dysfunctions Using a Multi-Body Dynamics Approach Andrew S. ... "Fully-Coupled Nonlinear 3-D Time-Domain Simulation of Drilling Dysfunctions Using a Multi-Body Dynamics Approach." Paper ... Using a multi-body dynamics (MBD) approach, drill string components are modeled in a physically intuitive manner. All nonlinear ... Traditional finite element (FE) methods used to analyze drill string dynamics are linear and operate in the frequency domain. ...
Nonlinear Dynamics @ FU Berlin: Cooperations
In the following we give links to those in Berlin, Germany and Europe which share many of our interests in nonlinear dynamics. ... Research Group on Laser Dynamics. *Max-Planck-Institute for Gravitational Physics (Albert-Einstein-Institute) International Max ... DFG Collaborative Research Center 555 on Complex Nonlinear Processes. *DFG Collaborative Research Center 647 on Space - Time - ... DFG Collaborative Research Center 910 on Control of self-organizing nonlinear systems: Theoretical methods and concepts of ...
Nonlinear economic growth dynamics in the context of a military arms race | Metz | Studia Universitatis Babeș-Bolyai Mathematica
Nonlinear Vibration Localization in Cyclic Structures - Dynamics Group
From nonlinear dynamics in general it is well known that there are certain mechanisms that may lead to nonlinearly localized ... In nonlinear vibrations, the amplitude-dependent frequency shifts of single nonlinear oscillators may lead to a reduced ... Which bring along novel nonlinear vibration phenomena. One class of such nonlinear vibrations are nonlinearly localized ... dynamics. While for many fields in science such nonlinear localization has been studied for a long time, and its relevance is ...
Non-linear grey-box modelling for heat dynamics of buildings - Fingerprint
- Welcome to DTU Research Database
Modeling and Approximation of Nonlinear Dynamics of Flapping Flight
... and control of nonlinear dynamics associated with flapping flight. ... and we can focus attention on flapping wing aerodynamics for such nonlinear systems. We study nonlinear modeling, ... In addition to complexities that arise from morphology of the animal, some of the external forces that influence the dynamics ... For this class of systems, the models derived from morphology of the skeleton are usually very high dimensional, nonlinear, and ...
Particle‐in‐cell experiments examine electron diffusion by whistler‐mode waves: 2. Quasi‐linear and nonlinear dynamics -...
... linear and nonlinear dynamics. Test particle codes indicate that electron dynamics due to interactions with low amplitude ... linear and nonlinear dynamics. Particle‐in‐cell experiments examine electron diffusion by whistler‐mode waves: 2. Quasi‐ ... the resonant interactions with higher amplitude waves cause significant nondiffusive dynamics as well as diffusive dynamics. ... When electron dynamics are extracted and analyzed over time scales shorter than T , we are able to isolate both the diffusive ...
Chaotic Analysis and Chaos Control of a Lateral Dynamics Vehicle Based on the Nonlinear Poincaré Map with Fuzzy Controller - ...
... firstly chaotic behavior of the lateral dynamics of vehicle is investigated by the use of numerical tools including Lyapunov ... Pashaei F, Abtahi S M. Chaotic Analysis and Chaos Control of a Lateral Dynamics Vehicle Based on the Nonlinear Poincaré Map ... Chaotic Analysis and Chaos Control of a Lateral Dynamics Vehicle Based on the Nonlinear Poincaré Map with Fuzzy Controller ... A robust Fuzzy system on the basis of nonlinear Ott-Grebogi-Yorke (OGY) method forms the control system. Closed-loop results of ...
Exponential stabilization of nonlinear driftless systems with robustness to unmodeled dynamics | ESAIM: Control, Optimisation...
The Dynamics, Bifurcation, and Practical Stability Analysis/Design of Nonlinear Microwave Circuits and Networks Part 2 | IEEETV
The Dynamics, Bifurcation, and Practical Stability Analysis/Design of Nonlinear Microwave Circuits and Networks Part 2 3 views ... The Dynamics, Bifurcation, and Practical Stability Analysis/Design of Nonlinear Microwave Circuits and Networks Part 2 ... The Dynamics, Bifurcation, and Practical Stability Analysis/Design of Nonlinear Microwave Circuits and Networks Part 2 ... The Dynamics, Bifurcation, and Practical Stability Analysis/Design of Nonlinear Microwave Circuits and Networks Part 2 ...
DynamicalChaosIntroduction to Nonlinear DynamicsApplications of Nonlinear DynamicsPhenomenaProcessesStochastic dynamicsOscillationsLinear and nonlinearHighly nonlinearApproximationTheoreticalSystemsBehaviorFluid dynamics2022StatisticalWaves1998MathematicsApproachStability analysisLocalizationAsymptoticTheoryPhysicsUltrafastRobustASMEMathematical2021GeometricInvariantControlPredictiveShiftsStudyElectronAnalysisAlgorithmModelingInteractionsOrdinaryMorphologyMechanismsSystemJournal
Dynamical4
- This book uses a hands-on approach to nonlinear dynamics using commonly available software, including the free dynamical systems software Xppaut, Matlab (or its free cousin, Octave) and the Maple symbolic algebra system. (tenlong.com.tw)
- We use tools from dynamical systems theory and statistical physics to comprehend the mechanisms behind the dynamics and changes of states in nonlinear systems. (google.com)
- Mother-infant interaction and quality of child s attachment: A nonlinear dynamical systems approach. (bvsalud.org)
- This unsolved problem of determining the long-term stability of given orbital configurations has a rich history, partially motivating the discovery of dynamical chaos and driving the development of non-linear dynamics. (lu.se)
Chaos4
- Nonlinear Dynamics, An International Journal of Nonlinear Dynamics and Chaos in Engineering Systems is a monthly peer-reviewed scientific journal covering all nonlinear dynamic phenomena associated with mechanical, structural, civil, aeronautical, ocean, electrical, and control systems. (wikipedia.org)
- In particular, we demonstrate that the "deterministic chaos" present in many nonlinear systems can impose fundamental limitations on our ability to predict behavior even when precisely defined mathematical models exist. (santafe.edu)
- M. Dichter, Student solutions manual for Nonlinear dynamics and chaos, Westview Press. (epfl.ch)
- Fractals are related to "chaos" (see NONLINEAR DYNAMICS) in that chaotic processes can produce fractal structures in nature, and appropriate representations of chaotic processes usually reveal self-similarity over time. (bvsalud.org)
Introduction to Nonlinear Dynamics1
- This course is an introduction to nonlinear dynamics with applications to biology targeted to junior/senior engineering students and 1st year graduate students in engineering and quantitative life sciences. (openwetware.org)
Applications of Nonlinear Dynamics1
- Theory and applications of nonlinear dynamics of extended systems including nonlinear waves, pattern formation, turbulence, self-organized criticality and networks. (umd.edu)
Phenomena3
- We discuss the extent to which recent improvements in our understanding of inherently nonlinear phenomena present challenges to the use of mathematical models in the analysis of environmental and socio-political issues. (santafe.edu)
- Which bring along novel nonlinear vibration phenomena. (tu-harburg.de)
- Conceptual, numerical, and experimental studies, based on a model system, are to be conducted to characterize and quantify the phenomena related with nonlinear vibration localization. (tu-harburg.de)
Processes6
- Special attention is attributed to nonlinear processes, to thin cells with nano-scaled inter-electrode gap, to non-equilibrium states and their relaxation to equilibrium, to the enhancement of the interface electrode polarization and capacity by charge pump through a complementary electrode etc. (eurekaselect.com)
- This is done in a statistical physicslike approach where one associates, to the spontaneous dynamics of the model, a natural notion of Gibbs distribution inherited from ergodic theory or stochastic processes. (aip.org)
- These results suggest that either (1) ENSO is not governed by low-dimensional nonlinear dynamics, or (2) noise related to local physical processes overwhelms the ENSO chaotic signal in the observational data. (uri.edu)
- While the major guiding principles of plasmonic waveguides are well understood, little is known about different nonlinear processes with plasmons so far. (bath.ac.uk)
- It is the purpose of this research to develop appropriate theories and explore fundamentally new nonlinear processes associated with light propagation in composite nano-structures consisting of metals and dielectrics. (bath.ac.uk)
- Processes can be used to further extend the consensus emergence models, allowing them to capture nonlinear dynamics, on both individual and group levels, in emergent processes. (lu.se)
Stochastic dynamics1
- We present results concerning geometric ergodicity and exponential stability of the unique invariant measures for two nonlinear stochastic dynamics: Langevin dynamics in the presence of singular potential functions, and the degenerate stochastic Lorenz 96 model. (iastate.edu)
Oscillations2
- Proceedings 1st European Nonlinear Oscillations Conference. (bris.ac.uk)
- booktitle = "Proceedings 1st European Nonlinear Oscillations Conference. (bris.ac.uk)
Linear and nonlinear2
- Further topics of the study are the emergence of extended domains of localized vibration, the transition regeion between zones of strong and weak or no vibration, and the interplay between linear and nonlinear localization mechanisms. (tu-harburg.de)
- All these problems are tackled with the help of a common numerical algorithm applied in both linear and nonlinear approximation. (eurekaselect.com)
Highly nonlinear2
- Since even a freely rotating rigid body with six degrees of freedom already leads to highly nonlinear system equations, a general analysis for the full system equations is not feasible. (springer.com)
- Closed-loop control of the firing rate of the neuron is thus desirable, but very challenging due to the underlying highly nonlinear dynamics. (researchsquare.com)
Approximation1
- A response approximation method for stochastically excited, nonlinear, dynamic systems is presented. (tue.nl)
Theoretical2
- The purpose of the Journal of Computational and Nonlinear Dynamics is to provide a medium for rapid dissemination of original research results in theoretical as well as applied computational and nonlinear dynamics. (asme.org)
- To achieve our goals, NoDE is supported by a big network of enthusiastic collaborators working on dynamics, applied mathematics, systems and synthetic biology, as well as in field and theoretical ecology. (google.com)
Systems14
- The journal serves as a forum for the exchange of new ideas and applications in computational, rigid and flexible multi-body system dynamics and all aspects (analytical, numerical, and experimental) of dynamics associated with nonlinear systems. (asme.org)
- The broad scope of the journal encompasses all computational and nonlinear problems occurring in aeronautical, biological, electrical, mechanical, physical, and structural systems. (asme.org)
- Rather recently, however, it has become more obvious that such cyclic systems also bear marked nonlinear properties. (tu-harburg.de)
- For this class of systems, the models derived from morphology of the skeleton are usually very high dimensional, nonlinear, and complex. (vt.edu)
- Second, by restricting the robotic systems to be anchored in an inertial frame, the robotic equations of motion are well understood, and we can focus attention on flapping wing aerodynamics for such nonlinear systems. (vt.edu)
- Exponential stabilization of nonlinear driftless affine control systems is addressed with the concern of achieving robustness with respect to imperfect knowledge of the system's control vector fields. (esaim-cocv.org)
- The course provides students with the tools to approach the study of nonlinear systems and chaotic dynamics. (epfl.ch)
- P.G. Drazin, Nonlinear systems, Cambridge University Press. (epfl.ch)
- Nonlinear dynamics are ubiquitous in natural and artificial systems. (google.com)
- The ultrafast optical dynamics of such hybrid plasmon-emitter systems have rarely been explored. (lu.se)
- The appearing problems are stiff, thus naturally leading to adaptive implicit time integration schemes and consequently the question of how to solve large nonlinear and linear equation systems efficiently. (lu.se)
- I will present our latest work combining our partial understanding of the dynamics in these systems with machine learning methods to significantly improve on previous efforts and computationally open up of the stability constrained characterization of exoplanet systems. (lu.se)
- Coherent multidimensional spectroscopy (CMDS) is a powerful nonlinear optical technique, which is used to study femtosecond dynamics in broad range of systems. (lu.se)
- Attoscience is the study of electron dynamics in quantum systems, such as atoms, molecules and solids, on a time scale down to a few attoseconds (1 as = 10^-18 s). (lu.se)
Behavior4
- The qualitative behavior of the nonlinear system can be analyzed, leading to slow-fast dynamics. (springer.com)
- However, it turns out that the linear dynamics of the full system cannot properly describe the qualitative behavior of the tippedisk. (springer.com)
- In this paper, firstly chaotic behavior of the lateral dynamics of vehicle is investigated by the use of numerical tools including Lyapunov exponent and bifurcation diagrams. (ac.ir)
- It is this nonlinear firing behavior together with firing rate that gives rise to synaptic plasticity and forms the basis of memory, perception, action, and behavior. (researchsquare.com)
Fluid dynamics3
- Article: Development of targeted compact nonlinear scheme with increasingly high order of accuracy Journal: Progress in Computational Fluid Dynamics, An International Journal (PCFD) 2020 Vol.20 No.1 pp.1 - 19 Abstract: In this paper we present general formulation of targeted compact nonlinear scheme (TCNS) with increasing order of accuracy. (inderscience.com)
- The first sub-model takes into consideration the fluid dynamics of the machine since the hammer is driven by compressed air. (cdc.gov)
- Specifically, the research is about time dependent nonlinear PDEs, particular those from computational fluid dynamics (CFD) and fluid structure interaction (FSI). (lu.se)
20221
- Nonlinear dynamics 2022 0 0. (cdc.gov)
Statistical1
- Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 84, no. 1 Pt 1 (2011). (duke.edu)
Waves7
- Test particle codes indicate that electron dynamics due to interactions with low amplitude incoherent whistler mode‐waves can be adequately described by quasi‐linear theory. (bas.ac.uk)
- However there is significant evidence indicating that higher amplitude waves cause electron dynamics not adequately described using quasi‐linear theory. (bas.ac.uk)
- We find that the electron dynamics agree well with the quasi‐linear theory diffusion coefficients for low amplitude incoherent waves with (B w,rms/B 0)2≈3.7·10−10, over a time scale T of the order of 1,000 gyroperiods. (bas.ac.uk)
- However, the resonant interactions with higher amplitude waves cause significant nondiffusive dynamics as well as diffusive dynamics. (bas.ac.uk)
- Therefore, the proper description of electron dynamics in response to wave‐particle interactions with higher amplitude whistler‐mode waves may require Fokker‐Planck equations that incorporate diffusive and advective terms. (bas.ac.uk)
- Instability of Nonlinear Periodic Waves in a Dispersive Medium. (sgu.ru)
- Kinetics of Nonlinear Waves in Dispersive Media. (sgu.ru)
19981
- Aljain, Corrie Modell, "Characterizing Enso with Nonlinear Dynamics" (1998). (uri.edu)
Mathematics2
- Mathematics can allow us to understand and sometimes predict these motions (dynamics). (google.com)
- He studies the mathematics of collective animal behaviour, social dynamics and mathematical biology. (lu.se)
Approach1
- Using a multi-body dynamics (MBD) approach, drill string components are modeled in a physically intuitive manner. (onepetro.org)
Stability analysis1
- Therefore, we simplify the equations of motion of the tippedisk in such a way that the qualitative dynamics are preserved in order to obtain a reduced model that will serve as the basis for a following nonlinear stability analysis. (springer.com)
Localization3
- While for many fields in science such nonlinear localization has been studied for a long time, and its relevance is widely acknowledged, for nonlinear mechanical vibrations the understanding is still comparatively limited. (tu-harburg.de)
- In nonlinear vibrations, the amplitude-dependent frequency shifts of single nonlinear oscillators may lead to a reduced coupling to neighbouring oscillators, which under certain conditions may result in full spatial localization of the vibration. (tu-harburg.de)
- We will aim at answering, under what system and loading conditions nonlinear vibration localization appears, and how robust or stable it is. (tu-harburg.de)
Asymptotic2
- An asymptotic theory for the nonlinear and dispersion managed solitons agrees well with the experimental data. (nist.gov)
- Nonlinear system / asymptotic stabilization / robust control / Chen-Fliess series. (esaim-cocv.org)
Theory5
- Interestingly, when considered over these appropriately shorter time scales (of the order of hundreds or tens of gyroperiods), the diffusive component of the dynamics agrees well with the predictions of quasi‐linear theory, even for wave amplitudes up to (B w,rms/B 0)2≈5.8·10−6. (bas.ac.uk)
- Quasi‐linear theory is based on fundamentally diffusive dynamics, but the evidence presented herein also indicates the existence of a distinct advective component. (bas.ac.uk)
- Despite the emphasis on computer calculations, theory is not neglected, and fundamental concepts from the field of nonlinear dynamics such as solution maps and invariant manifolds are presented. (tenlong.com.tw)
- This course is intended for advanced study of the theory of nonlinear dynamics and its application. (edu.au)
- Research on the theory of nonlinear resonance and stochasticity. (sgu.ru)
Physics1
- Semiconductor Superlattices: A model system for nonlinear transport , Physics Reports 357 , 1-111 (2002) (Review article) . (lu.se)
Ultrafast1
- Ultrafast dynamics and third-order nonlinear optical studies of tetraoxa[22]porphyrin(2.1.2.1)s are reported using a single beam Z-scan technique with femtosecond (fs) and nanosecond (ns) pulses at respective near-IR and visible wavelengths. (rsc.org)
Robust3
- A robust Fuzzy system on the basis of nonlinear Ott-Grebogi-Yorke (OGY) method forms the control system. (ac.ir)
- Next, a dynamic inversion nonlinear controller, a robust incremental dynamic inversion controller, and a model predictive controller are derived to directly regulate the nonlinear neuron dynamics in terms of controlled firing. (researchsquare.com)
- The synthesis of lead, lag, lead-lag, dynamic inversion, model predictive control-based feedback controllers over the nonlinear dynamics of the neuron led to controlled firing and a fast response that was robust to stochastic synaptic noise. (researchsquare.com)
ASME1
- Collection of Technical Papers Aiaa/Asme/Asce/Ahs/Asc Structures, Structural Dynamics and Materials Conference (2011). (duke.edu)
Mathematical2
20211
- Applied Nonlinear Dynamics}, volume = {17}, number = {1}, url = {https://andjournal.sgu.ru/sites/andjournal.sgu.ru/files/text-pdf/2021/08/1_2009-150-161.pdf}, address = {Saratov State University, ul. (sgu.ru)
Geometric2
- All nonlinear geometric and inertial effects are properly accounted for, without restrictions on angular displacements or angular rates. (onepetro.org)
- We prove geometric ergodicity of the 4-dimensional degenerate stochastic Lorenz 96 dynamics by means of a partitioning of the state space at high energies, and relevant pathwise computations of properly scaled dynamics in each partition. (iastate.edu)
Invariant1
- We prove hypocoercivity in the singular Langevin dynamics by means of a modified, but equivalent, norm reliant on the existence of a Poincaré inequality in both the space and momentum marginals of the invariant measure. (iastate.edu)
Control4
- We study nonlinear modeling, identification, and control problems that feature the above complexities. (vt.edu)
- This document summarizes research progress and plans that focuses on two key aspects of modeling, identification, and control of nonlinear dynamics associated with flapping flight. (vt.edu)
- Modeling SARS-CoV-2 and HBV co-dynamics with optimal control. (cdc.gov)
- Quantum control of HHG is a vast subject with applications from the microscopic atomic scale, where electron correlation and molecular dynamics, to the macroscopic scale of optics. (lu.se)
Predictive1
- When applied to observational ENSO data, the Barahona and Poon algorithm indicates that low-order nonlinear mapping functions have predictive power which is not significantly different from linear models. (uri.edu)
Shifts1
- In the article we offer to consider case of a flexural deformation shifts of a tool when they are essential for nonlinear dynamics of cutting process. (sgu.ru)
Study3
- By combining the study of these two observables, it becomes possible to study some eigenvector correlations.The second part concerns the study of eigenvalue distribution of nonlinear models of random matrices. (hal.science)
- These models appear in the study of random neural networks and correspond to a nonlinear version of sample covariance matrices in the sense that a nonlinear function, called the activation function, is applied entrywise to the matrix. (hal.science)
- Here, we study those dynamics by interferometrically probing nonlinear optical emission from individual porous gold nanosponges infiltrated with zinc oxide (ZnO) emitters. (lu.se)
Electron2
- When electron dynamics are extracted and analyzed over time scales shorter than T , we are able to isolate both the diffusive and nondiffusive (advective) dynamics. (bas.ac.uk)
- Our results demonstrate that the analysis of diffractive ρ production in future electron - ion colliders will be important to understand the nonlinear QCD dynamics. (lu.se)
Analysis1
- The analysis of possible population dynamics development was performed by two qualitatively different discrete sampling techniques (Bubnov-Galerkin's method and grid method). (sgu.ru)
Algorithm1
- In contrast, when the algorithm is applied to correspondingly sampled data from the Vallis model, the algorithm shows the presence of nonlinear determinism, even when these data are strongly contaminated with noise. (uri.edu)
Modeling1
- The interview includes 15 questions on topics ranging from nonlinear dynamics, ecological modeling, and heterogenous agents. (degruyter.com)
Interactions1
- Nonlinear deformations are a key ingredient for applications of rheologically complex materials, e.g. for the processing of polymeric materials stretching, orientation, dissentaglement of polymer chains occurs, with the interactions between flow field and constituents dictating the overall flow dynamics and subsequent material properties/performance. (lu.se)
Ordinary2
- The inversion phenomenon of the tippedisk can be modeled by a rigid eccentric disk in permanent contact with a flat support, and the dynamics of the system can therefore be formulated as a set of ordinary differential equations. (springer.com)
- It is most common, perhaps, that this process generates a set of coupled nonlinear ordinary or partial differential equations. (vt.edu)
Morphology2
- In addition to complexities that arise from morphology of the animal, some of the external forces that influence the dynamics of animal motion are very hard to model. (vt.edu)
- The effects of orientation dynamics and morphological fingerprinting are highlighted, with rheological percolation thresholds determined with superior sensitivity using nonlinear material parameters and nonlinear features hinting at the filler morphology of percolated network dynamic response. (lu.se)
Mechanisms1
- From nonlinear dynamics in general it is well known that there are certain mechanisms that may lead to nonlinearly localized dynamics. (tu-harburg.de)
System3
- Herein, the output of the nonlinear system is approximated by a finite-order Volterra series. (tue.nl)
- The original, nonlinear system is replaced by a bilinear system in order to determine the kernels of this Volterra series. (tue.nl)
- Regular and chaotic dynamics of two-ring phase locked system. (sgu.ru)
Journal4
- It should not be confused with the similarly named Russian journal Nelineinaya Dinamika (or the Russian Journal of Nonlinear Dynamics). (wikipedia.org)
- CND - Journal of Computational and Nonlinear Dynamics has been added to your cart. (asme.org)
- International Journal of Structural Stability and Dynamics 12, no. 2 (2012): 403-421. (duke.edu)
- International Journal of Structural Stability and Dynamics 11, no. 6 (2011). (duke.edu)
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