Recurrence quantification analysis (RQA) is a method of nonlinear data analysis (cf. chaos theory) for the investigation of dynamical systems. It quantifies the number and duration of recurrences of a dynamical system presented by its phase space trajectory. The recurrence quantification analysis was developed in order to quantify differently appearing recurrence plots (RPs) based on the small-scale structures therein. Recurrence plots are tools which visualise the recurrence behaviour of the phase space trajectory of dynamical systems. They mostly contain single dots and lines which are parallel to the mean diagonal (line of identity, LOI) or which are vertical/horizontal. Lines parallel to the LOI are referred to as diagonal lines and the vertical structures as vertical lines. Because an RP is usually symmetric, horizontal and vertical lines correspond to each other, and, hence, only vertical lines are considered. The lines correspond to a typical behaviour of the phase space trajectory: ...
The International Journal of Nonlinear Analysis and Applications (IJNAA) The International Journal of Nonlinear Analysis and Applications (IJNAA), a publicatio
How is Bubble and Drop Nonlinear Dynamics abbreviated? BDND stands for Bubble and Drop Nonlinear Dynamics. BDND is defined as Bubble and Drop Nonlinear Dynamics rarely.
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This paper deals with the study of the nonlinear dynamics of a rotating flexible link modeled as a one dimensional beam, undergoing large deformation and with geometric nonlinearities. The partial differential equation of motion is discretized using a finite element approach to yield four nonlinear, nonautonomous and coupled ordinary differential equations (ODEs). The equations are nondimensionalized using two characteristic velocities-the speed of sound in the material and a velocity associated with the transverse bending vibration of the beam. The method of multiple scales is used to perform a detailed study of the system. A set of four autonomous equations of the first-order are derived considering primary resonances of the external excitation and one-to-one internal resonances between the natural frequencies of the equations. Numerical simulations show that for certain ranges of values of these characteristic velocities, the slow flow equations can exhibit chaotic motions. The numerical ...
The lectures cover the main concepts of nonlinear dynamics, emphasizing characterization of complex networks. First, the basic ideas of nonlinear dynamics, such as description of nonlinear systems, stability analysis, bifurcations and attractors will be introduced. Further, the main concepts of the theory of complex networks will be explained. A special attention will be paid to synchronization phenomena including partial synchronization patterns. Synchronization is one of the fundamental phenomena in nature. Fireflies flashing in unison, coordinated firing of pacemaker cells in our hearts, fish swimming in a synchronized swarm - these are just a few real-world examples of self-organization. We will discuss synchronization in various systems ranging from periodic oscillators to chaotic and stochastic systems, from two coupled units to complex networks. Various applications in different fields of science including physics, chemistry, biology and engineering will be discussed. ...
The nonlinear dynamics we have described in the cVEP resemble cortical gain control phenomena that have been reported previously for cortical responses to achromatic signals (Albrecht, Geisler, Frazor, & Crane, 2002; Carandini et al., 1997; Ohzawa et al., 1982). Thus it is well known that there are large phase advances and speeding up of time-to-peak of responses of single cortical cells when the contrast of achromatic stimuli is increased (Albrecht et al., 2002; Carandini & Heeger, 2011; Carandini et al., 1997). Such nonlinear dynamics have been ascribed to the action of a cortical contrast gain control, also called normalization. There are different possible models of cortical normalization. Some authors have maintained that normalization is not even a cortical phenomenon but occurs precortically (Freeman et al., 2002), though we remind the reader that such earlier proposals were based on results in the cat cortex and visual pathway where there is no contrast-linear counterpart to the ...
Abstract: Delay embeddings of time series data have emerged as a promising coordinate basis for data-driven estimation of the Koopman operator, which seeks a linear representation for observed nonlinear dynamics. Recent work has demonstrated the efficacy of Dynamic Mode Decomposition (DMD) for obtaining finite-dimensional Koopman approximations in delay coordinates. In this paper we demonstrate how nonlinear dynamics with sparse Fourier spectra can be (i) represented by a superposition of principal component trajectories (PCT) and (ii) modeled by DMD in this coordinate space. For continuous or mixed (discrete and continuous) spectra, DMD can be augmented with an external forcing term. We present a method for learning linear control models in delay coordinates while simultaneously discovering the corresponding exogeneous forcing signal in a fully unsupervised manner. This extends the existing DMD with control (DMDc) algorithm to cases where a control signal is not known a priori. We provide ...
Nonlinear analysis of the longitudinal flight dynamics of a transport airplane. . Biblioteca virtual para leer y descargar libros, documentos, trabajos y tesis universitarias en PDF. Material universiario, documentación y tareas realizadas por universitarios en nuestra biblioteca. Para descargar gratis y para leer online.
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In this paper, we investigate the chaotic behavior of the biological sequences among the different species. Throughout this work, we have characterized the biological sequences according to their moment invariant, correlation dimension, and largest Lyapunov exponent estimates. We have applied our model to a number of human and mouse genomes encoded into a set of integers (time series) using a plain table mapping scheme. Our results indicate that the nonlinear dynamical characteristics have yielded significant differences between the sequences of the different species. That is, we have been able to classify the different genome sequences according to their chaotic parameters estimates. On the other hand, through our investigation we have found that the use of the chaotic modeling of the biological sequences could open new frontiers in the sequence similarity search ...
Many systems in nature spontaneously form nontrivial spatial structures: ice flowers on a window or ripples on a beach are simple examples of large scale patterns that occur in nature, but there are also numerous examples of spontaneous pattern formation that occur in non-equilibrium systems in physics, astronomy, chemistry and biology. The behavior of such systems is often highly nonlinear, and hence their description usually involves nonlinear analysis, in particular the analysis of nonlinear partial differential equations. This course will give an introduction to both the phenomena that are encountered, as well as to some of the theoretical models introduced for them and the mathematical techniques needed to analyze their nonlinear behavior.. ...
Many systems in nature spontaneously form nontrivial spatial structures: ice flowers on a window or ripples on a beach are simple examples of large scale patterns that occur in nature, but there are also numerous examples of spontaneous pattern formation that occur in non-equilibrium systems in physics, astronomy, chemistry and biology. The behavior of such systems is often highly nonlinear, and hence their description usually involves nonlinear analysis, in particular the analysis of nonlinear partial differential equations. This course will give an introduction to both the phenomena that are encountered, as well as to some of the theoretical models introduced for them and the mathematical techniques needed to analyze their nonlinear behavior.. ...
This paper examines the importance of using nonlinear methods to account for the zero lower bound (ZLB) on the Feds policy rate. We estimate three models with
TY - GEN. T1 - Non-linear model reduction for metabolic networks with multiple time scales. AU - Gerdtzen, Ziomara P.. AU - Daoutidis, Prodromos. AU - Hu, Wei-Shou. PY - 2005/12/1. Y1 - 2005/12/1. N2 - We present a method for obtaining non-stiff non-linear reduced-order models for metabolic networks, which exhibit dynamics in multiple time scales. The method is based on the successive application of singular perturbation arguments, starting from the fastest time scale and proceeding to the slowest one. The method is successfully applied to a detailed model of central carbon metabolism in human erythrocytes.. AB - We present a method for obtaining non-stiff non-linear reduced-order models for metabolic networks, which exhibit dynamics in multiple time scales. The method is based on the successive application of singular perturbation arguments, starting from the fastest time scale and proceeding to the slowest one. The method is successfully applied to a detailed model of central carbon metabolism ...
TY - JOUR. T1 - Gradient-consistent non-linear model of the generation of ultrasound in the propagation of seismic waves. AU - Krylov, A. L.. AU - Mazur, N. G.. AU - Nikolayevskii, V. N.. AU - El, G. A.. PY - 1993. Y1 - 1993. N2 - The equations of the propagation of weak non-linear waves are obtained by a detailed analysis of the gradient-consistent micropolar model of a granular continuous medium. The high-frequency mode of oscillation is associated with ultrasonic waves, and the low-frequency mode is associated with the usual seismic waves in rocks. The evolution equations that include the case of long-wave-short-wave resonance are obtained by an asymptotic consideration. This resonance corresponds to the case of the generation of ultrasound (noise) by travelling seismic waves.. AB - The equations of the propagation of weak non-linear waves are obtained by a detailed analysis of the gradient-consistent micropolar model of a granular continuous medium. The high-frequency mode of oscillation is ...
RUST, T.; SCHOEMAN, S.J.; VAN DER WESTHUIZEN, J. and VAN WYK, J.B.. Non-linear model analysis of categorical traits related to female reproduction efficiency in beef cattle. S. Afr. j. anim. sci. [online]. 2009, vol.39, n.4, pp.260-266. ISSN 2221-4062.. The utilization of non-linear threshold models and linear animal models to estimate variance components for categorical reproductive traits in beef cattle was investigated. Three traits, retention (RET), stayability (STAY) and calf tempo (CT) were defined. The data set consisted of 36 880 Afrikaner beef cattle measurements recorded over a period of 10 years. After editing, the records of 7 746 females from 473 sires were available for the genetic parameter estimation for RET. The corresponding number of records for STAY and CT were 3 018 (243 sires) and 7 653 (465 sires), respectively. Using GFCAT, sire variances for RET, STAY and CT were estimated as 0.202, 0.072 and 0.114, respectively. With error variances pre-set to one, the heritability ...
Computational and Mathematical Methods in Medicine is a peer-reviewed, Open Access journal that publishes research and review articles focused on the application of mathematics to problems arising from the biomedical sciences. Areas of interest include gene therapy, cell kinetics, pharmacokinetics, chemotherapy, oncology, developmental biology, wound healing, physiology, heart modelling, cardiovascular and lung dynamics, neurobiology, computational neuroscience, biomechanics, biomedical statistics, image analysis, epidemiology, immunology, time series analysis, extracellular matrix properties and signalling, and tissue engineering.
In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input.[1][2][3] Nonlinear problems are of interest to engineers, biologists,[4][5][6] physicists,[7][8] mathematicians, and many other scientists because most systems are inherently nonlinear in nature.[9] Nonlinear dynamical systems, describing changes in variables over time, may appear chaotic, unpredictable, or counterintuitive, contrasting with much simpler linear systems. Typically, the behavior of a nonlinear system is described in mathematics by a nonlinear system of equations, which is a set of simultaneous equations in which the unknowns (or the unknown functions in the case of differential equations) appear as variables of a polynomial of degree higher than one or in the argument of a function which is not a polynomial of degree one. In other words, in a nonlinear system of equations, the equation(s) to be solved cannot be written as a linear combination ...
TY - GEN. T1 - Non-linear model fitting to parameterize diseased blood vessels. AU - La Cruz, Alexandra. AU - Šrámek, Miloš. AU - Strakat, Matúš. AU - Gröller, Eduard. AU - Köchl, Arnold. AU - Fleischmann, Dominik. PY - 2004. Y1 - 2004. N2 - Accurate estimation of vessel parameters is a prerequisite for automated visualization and analysis of healthy and diseased blood vessels. The objective of this research is to estimate the dimensions of lower extremity arteries, imaged by computed tomography (CT). These parameters are required to get a good quality visualization of healthy as well as diseased arteries using a visualization technique such as curved planar reformation (CPR). The vessel is modeled using an elliptical or cylindrical structure with specific dimensions, orientation and blood vessel mean density. The model separates two homogeneous regions: Its inner side represents a region of density for vessels, and its outer side a region for background. Taking into account the point ...
Read chapter Stability and Accuracy of a Non-Linear Model for the Wave Resistance Problem: The Proceedings: Fifth International Conference on Numerical Sh...
Optimal Experimental Design for Non-Linear Models von Christos P. Kitsos - Englische Bücher zum Genre Mathematik günstig & portofrei bestellen im Online Shop von Ex Libris.
Modeling Development and Numerical Simulation of Transient Nonlinear Behaviors of Electric sensitive Hydrogel Membrane under an External Electric Field Abstract.
Recently, we published a theoretical analysis of the nonlinear behavior of a MEMS variable capacitor, but until now these formulas where not confirmed with
deg / h due to nonlinear coupling between the countertraveling modes. This coupling arises due to the backreflection of modes from moving index gratings, induced by rotation. Lock-in threshold is directly proportional to the strength of nonlinear coupling and spatial overlap of the modes energy densities with periodic index perturbations.. © 2016 Optical Society of America. Full Article , PDF Article ...
This dissertation articulates concepts from different disciplines and incorporates a comprehensive study of complex systems. Many dynamical processes on complex structures of interactions exhibit forms of emergent behaviors, often unspecified in the equations of motion. In consequence, this thesis can be divided into two parts: First, we introduce many basic concepts of Network Science, essential to understand the main findings of our research. Second, we present all of the results of nonlinear dynamics on top of synthetic and real graphs, providing a comparative analysis between the behaviors of our simulated configurations and the phenomena observed in electronic, neuronal and social systems. In short, once both constituents have been implemented and optimized, the chief goal is to investigate and analyze thoroughly the models of nonlinear dynamics in such systems, incorporating aspects such as analytical predictions, the appearance of collective complex behaviors.|br /|SYSTEMS OF INTEREST|br /|-
The cost of releasing a new drug on the market has increased rapidly in the last decade. The reasons for this increase vary with the drug, but the need to make correct decisions earlier in the drug development process and to maximize the information gained throughout the process is evident.. Optimal experimental design (OD) describes the procedure of maximizing relevant information in drug development and drug treatment processes. While various optimization criteria can be considered in OD, the most common is to optimize the unknown model parameters for an upcoming study. To date, OD has mainly been used to optimize the independent variables, e.g. sample times, but it can be used for any design variable in a study.. This thesis addresses the OD of multiple continuous or discrete design variables for nonlinear mixed effects models. The methodology for optimizing and the optimization of different types of models with either continuous or discrete data are presented and the benefits of OD for such ...
Goodness of Fit in Nonlinear Dynamics: Mis-specified Rates or Mis-specified States?. Giles Hooker, Stephen P. Ellner(Submitted on 2 Dec 2013). This paper introduces tests to uncover the nature of lack of fit in ordinary differential equation models (ODEs) proposed for data. We present a hierarchy of three possible sources of lack of fit: unaccounted-for stochastic variation, mis-specification of functional forms in the rate equations, and missing dynamical variables in the description of the system. We represent lack of fit by allowing some parameters to vary over time, and propose generic testing procedures that do not rely on specific alternative models. Our hypotheses are expressed in terms of nonparametric relationships among latent variables, and the tests are carried out through a combined residual bootstrap and permutation methods. We demonstrate the effectiveness of these tests on simulated data, and on real data from laboratory ecological experiments and electro-cardiogram ...
In single degree-of-freedom oscillators, impacts can occur with a barrier, while in a system with multiple degrees-of-freedom, one can additionally observe impacts among interacting bodies. On the one hand, impacts are intrinsic for the operations of many engineering devices. On the other hand, impacts may induce dangerous forces or perturb operations in systems where we expect to have smooth dynamics. In both situations, a deep understanding of the system dynamics can help predict the system behavior and also form a picture of the implications of impacts. Systems experiencing impacts are part of a large group of systems modeled by discontinuous differential equations; their dynamics is also interesting from a theoretical standpoint. Finding accurate numerical solutions of a discontinuous system of equations remains a challenging task in the field of nonlinear dynamics. There are many open problems associated with numerical and analytical investigations of impact oscillators, for example, the ...
The peripheral skin microcirculation reflects the overall health status of the cardiovascular system and can be examined non-invasively by laser methods to assess early cardiovascular disease (CVD) risk factors, i.e. oxidative stress and endothelial dysfunction. Examples of methods used for this task are the laser Doppler flowmetry (LDF) and laser fluorescence spectroscopy (LFS), which respectively allow tracing blood flow and the amounts of the coenzyme NAD(P)H (nicotamide adenine dinucleotide) that is involved in the cellular production of ATP (adenosine triphosphate) energy. In this work, these methods were combined with iontophoresis and PORH (post-occlusive reactive hyperaemia) reactive tests to assess skin microvascular function and oxidative stress in mice and human subjects. The main focus of the research was exploring the nonlinear dynamics of skin LDF and NAD(P)H time series by processing the signals with the wavelet transform analysis. The study of nonlinear fluctuations of the ...
In order to model neuronal behavior or to interpret the results of modeling studies, neuroscientists must call upon methods of nonlinear dynamics. This book offers an introduction to nonlinear dynamical systems theory for researchers and graduate students in neuroscience. It also provides an overview of neuroscience for mathematicians who want to learn the basic facts of electrophysiology.. Dynamical Systems in Neuroscience presents a systematic study of the relationship of electrophysiology, nonlinear dynamics, and computational properties of neurons. It emphasizes that information processing in the brain depends not only on the electrophysiological properties of neurons but also on their dynamical properties. The book introduces dynamical systems, starting with one- and two-dimensional Hodgkin-Huxley-type models and continuing to a description of bursting systems. Each chapter proceeds from the simple to the complex, and provides sample problems at the end. The book explains all necessary ...
Nonlinear Dynamics in Goettingen, The Max Planck Institute for Dynamics and Self-Organization, Germany. Research: Quantumchaos, Epidemiology, and Computational Neuroscience
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Research Associate in Collective Nonlinear Dynamics of Power Grid Networks in Fixed Term, Research Associate, Engineering & Technology with TECHNISCHE UNIVERSITAT DRESDEN (TU DRESDEN). Apply Today.
Presents state-of-the-art applications in nonlinear dynamics and synchronization Discusses selected applications in electrical engineering,
Behn, U., Brede, Markus and Richter, Joachim (2004) Nonlinear dynamics and statistical physics of models for the immune system. In, Deutch, A., Howard, J., Falcke, M. and Zimmermann, W. (eds.) Function and Regulation of Cellular Systems. Basel, CH. Birkhäuser, pp. 399-410. ...
Nonlinear Dynamics Ltd, the world leading developer of analysis solutions for proteomics, biomarker discovery and clinical diagnostics, has signed an agreement with UVP, LLC, a global leader in life science imaging for academic, biopharmaceutical and biotechnology applications.
The seminar offers perspectives on our current research in the area of Nonlinear Dynamics and Control. The seminar is particularly suitable for BSc and MSc students looking for a final project. Students, who want to obtain a Seminarschein, are welcome as well ...
This paper describes the experimental identifi- cation of the parameters of the Twin Rotor MIMO System (TRMS) non-linear model using data collected from the real lab set-up. From this non-linear model, a quasi-linear parameter varying (quasi-LPV) model has also been derived using a state transformation. This quasi-LPV model is approximated with a polytopic model using the bounding box approach. Such a model can later be used for control design. The model parameters have been calibrated by means of non-linear least- squares identification approach. Once the calibrated non-linear model has been obtained, a simulator has been built and validated against real data showing satisfactory results when compared to real data ...
Author: Zhou, S. et al.; Genre: Journal Article; Published in Print: 2001; Title: Analysis of the nonlinear dynamics of a direct methanol fuel cell
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ABSTRACT: A mesocosm experiment was performed in order to observe the behaviour of an aquatic community under stable external conditions. The hypothesis was that the community would show temporal fluctuations that correspond to the principles of deterministic chaos. Water from a brackish (9 psu) location was kept from 31 March 1989 to 11 July 1990 in a 100 l mesocosm under artificial laboratory conditions to develop a species-depleted climax community of plankton. The mesocosm was reared for a further period of 1764 d (12 July 1990 to 11 May 1995) under controlled light and temperature conditions and sampled in short intervals of 3 to 4 d. During the period of observations there were no changes in species composition, but strong fluctuation in biomass occurred. The biomass data for picophytoplankton, nanophytoplankton, copepods and rotifers were used to check the systems dynamics for chaotic behaviour by recurrence quantification analysis (RQA), a new method which is applied here to analyse ...
Nonlinear springs enhance the performance of many applications including prosthetics, microelectromechanical systems devices, and vibration absorption systems. This paper describes a comprehensive approach to developing compliant elements of prescribed nonlinear stiffness. It presents a generalized methodology for designing a single planar nonlinear spring for a prescribed load-displacement function. The springs load-range, displacement-range, and nonlinear behavior are matched using this methodology, while also addressing stress, material, stability, and space constraints. Scaling guidelines are included within the optimization to relax the constraints on the solution space. Given the nonlinear nature of the spring designs, this paper further investigates their function in new configurations. Compliant structures with customized elastic properties are constructed by exploiting symmetry and by arranging nonlinear springs in series and/or in parallel. Scaling guidelines are used to meet new ...
This book is an outstanding text describing and detailing chaotic systems from a classical mechanics viewpoint. It is clear, well-organized, well-written, and filled with examples, pictures, graphs, and problems for different chaotic systems. Whether the reader just reads through it or, better still, if he/she works through the examples, this book will give the reader a broad background on chaotic systems and provide analytical skills and insights necessary for independent study or research.. The list of chapters can be seen in the table of contents . Each chapter is filled with explanatory text, figures that are extremely well-done and illustrative (more so than I have seen in other similar books), and problems that take the concepts further than the text. At the back of the book there are solutions to most, but not all, of the problems.. Here is why I found this book so good.. The introductory chapter shows how chaos is prevalent in nature, giving simple physical examples of it. Examples ...
This is a set of easy-to-read lecture notes for a short first-year Ph.D. student course on Applied Dynamical Systems, which was given at the London Taught Course Centre in Spring 2008. The notes cover five hours of lectures and do not require any preknowledge on dynamical systems. The first part introduces to deterministic chaos in one-dimensional maps in form of Ljapunov exponents and the metric entropy. The second part first outlines the concept of deterministic diffusion. Then the escape rate formalism for deterministic diffusion, which expresses the diffusion coefficient in terms of the above two chaos quantities, is worked out for a simple map. The notes conclude with a very brief sketch of anomalous diffusion.
TY - GEN. T1 - Noninteracting control of nonlinear systems based on relaxed control. AU - Jayawardhana, B.. N1 - Relation: - Rights: -. PY - 2010. Y1 - 2010. N2 - In this paper, we propose methodology to solve noninteracting control problem for general nonlinear systems based on the relaxed control technique proposed by Artstein. For a class of nonlinear systems which cannot be stabilized by smooth feedback, a state-feedback relaxed control can be designed to decouple the system into several SISO or MIMO systems and simplify the controller design.. AB - In this paper, we propose methodology to solve noninteracting control problem for general nonlinear systems based on the relaxed control technique proposed by Artstein. For a class of nonlinear systems which cannot be stabilized by smooth feedback, a state-feedback relaxed control can be designed to decouple the system into several SISO or MIMO systems and simplify the controller design.. KW - relaxed control. KW - noninteracting control ...
Vector Lyapunov theory has been developed to weaken the hypothesis of standard Lyapunov theory in order to enlarge the class of Lyapunov functions that can be used for analyzing system stability. In this paper, we extend the theory of vector Lyapunov functions by constructing a generalized compariso.... Full description. ...
For evaluating performance of nonlinear features and iterative and non-iterative classification algorithms (i.e. kernel support vector machine (KSVM), random forest (RaF), least squares SVM (LS-SVM) and multi-surface proximal SVM based oblique RaF (ORaF) for ECG quality assessment we compared the four algorithms on 7 feature schemes yielded from 27 linear and nonlinear features including four features derived from a new encoding Lempel-Ziv complexity (ELZC) and the other 26 features. Seven feature schemes include the first scheme consisting of 7 waveform features, the second consisting of 15 waveform and frequency features, the third consisting of 19 waveform, frequency and approximate entropy (ApEn) features, the fourth consisting of 19 waveform, frequency and permutation entropy (PE) features, the fifth consisting of 19 waveform, frequency and ELZC features, the sixth consisting of 23 waveform, frequency, PE and ELZC features, and the last consisting of all 27 features. Up to 1500 mobile ECG ...
Nonlinear model reduction: discrete optimality and time parallelism Large-scale models of nonlinear dynamical systems arise in applications ranging from compressible fluid dynamics to structural dynamics. Due to the large computational cost incurred by these models, it is impractical to use them in time-critical scenarios such as control, design, uncertainty quantification. Model reduction aims to mitigate this computational burden. To date, reduced-order models (ROMs) for relatively simple models (e.g., linear-time-invariant systems; elliptic, parabolic, and linear hyperbolic PDEs) have been widely adopted, as researchers have developed methods that are accurate, reliable, and certified. In contrast, model reduction for nonlinear dynamical systems lacks these assurances and thus remains in its infancy; the most common method - POD-Galerkin - is often unstable. This talk will describe several advances that have made nonlinear model reduction viable for a new frontier of problems. However, doing ...