• I'm still keen on looking at dynamical systems, but it's probably going to be ergodic theory/symbolic dynamics/complex dynamics. (stackexchange.com)
  • In contrast to the heuristic approach of the recurrence quantification analysis, which depends on the choice of the embedding parameters, some dynamical invariants as correlation dimension, K2 entropy or mutual information, which are independent on the embedding, can also be derived from recurrence plots. (wikipedia.org)
  • H exponents show a long-range correlations (1/ f noise), and recurrence measures (percent determinism, maximum line, entropy, and trend), show a deterministic structure of variability being characteristic of self-organizing systems. (frontiersin.org)
  • The main attention will be paid to important dynamical phenomena and related results: periodicity, recurrence, minimality and transitivity, complexity measured by topological entropy, invariant measure, measure-theoretical entropy and variational principle, ergodicity and mixing. (cuni.cz)
  • The aim of this paper is to extend the $ q $-entropy from symbolic systems to a general topological dynamical system. (aimsciences.org)
  • occurrence of Chimera states in one layer due to the influence of another layer in multiplex recurrence networks. (iisertvm.ac.in)
  • an integrated approach to analyze the multi-lead ECG data is possible using multiplex recurrence networks (MRNs) constructed from the embedded dynamics from channel wise data. (iisertvm.ac.in)
  • The visual appearance of a recurrence plot gives hints about the dynamics of the system. (wikipedia.org)
  • In 1977, Leon Glass and Michael C. Mackey introduced the idea that certain diseases, which they labeled dynamical diseases, arise when an intact physiological control system operates in a range of control parameters that leads to abnormal dynamics and human pathology. (aip.org)
  • How to go about studying chaos theory/dynamical systems/fluid dynamics in grad school with a physics background? (stackexchange.com)
  • I'm turning to you as I find myself in need of help as to how to best go about studying something related to chaos theory/dynamical systems/fluid dynamics in postgraduate school. (stackexchange.com)
  • begingroup$ I would recommend looking into the courses at MIT Opencourseware and looking to see which books they use and the pre-requisites for the areas of chaos, dynamical systems and fluid dynamics. (stackexchange.com)
  • To get at the question of self-organization, reaction times were submitted to a detrended fluctuation analysis and a recurrence quantification analysis. (frontiersin.org)
  • Specifically, we will focus on the following methods: Recurrence Quantification Analyses (RQA), Fractal Analysis (FA), and Convergent Cross-Mapping (CCM). (leuphana.de)
  • He specializes in dynamical analyses of naturalistic human interactions, with a focus on Recurrence Quantification Analysis. (leuphana.de)
  • Caused by characteristic behaviour of the phase space trajectory, a recurrence plot contains typical small-scale structures, as single dots, diagonal lines and vertical/horizontal lines (or a mixture of the latter, which combines to extended clusters). (wikipedia.org)
  • The nonlinear interaction of the subsystems of speech production system brings in dynamical transitions from unvoiced to voiced speech and vice versa during continuous speech production. (amrita.edu)
  • Moreover, the recurrence of states, in the meaning that states are again arbitrarily close after some time of divergence, is a fundamental property of deterministic dynamical systems and is typical for nonlinear or chaotic systems (cf. (wikipedia.org)
  • use of machine learning algorithms applied to measures of recurrence networks and nonlinear time series analysis to differentiate between classes of close binary stars. (iisertvm.ac.in)
  • These are class notes written by Evans M. Harrell II of Georgia Tech. They are suitable for an introductory course on dynamical systems and chaos, taken by mathematicians, engineers, and physicists. (mathphysics.com)
  • Recurrence plots have been increasingly used to evaluate complex dynamic systems of which the human body is an excellent model. (bvsalud.org)
  • The different quantitative and qualitative elements of recurrence plots in health, disease, and death were analysed. (bvsalud.org)
  • This study was conducted to determine a simple method of detecting homeostasis impairment based on heart rate variability and recurrence plots. (bvsalud.org)
  • The quantitative and qualitative evaluation of recurrence plots allowed the selection of two variables (standard deviation of the RR normal intervals (SDNN) and the average length of the vertical lines (trapping time)), that when correlated in a phase space, discriminate individuals with adequate autonomic control (healthy children and adults), from those with autonomic systems compromised by immaturity or progressive loss of function. (bvsalud.org)
  • Chaotic dynamical systems are often (if not always) associated with fractals. (fact-index.com)
  • At a recurrence the trajectory returns to a location in phase space it has visited before up to a small error ε {\displaystyle \varepsilon } (i.e., the system returns to a state that it has before). (wikipedia.org)
  • Phase space reconstruction is not essential part of the recurrence plot (although often stated in literature), because it is based on phase space trajectories which could be derived from the system's variables directly (e.g., from the three variables of the Lorenz system). (wikipedia.org)
  • The recurrence spectra are computed for a few selected scaled energies and the results demonstrate that the scaled energy dominates the dynamical properties of system. (epj.org)
  • For the first time, an autonomous ordinary differential equation on a differentiable manifold \(M\ ,\) also called a vector field, flow, or dynamical system on \(M\ ,\) was considered from the point of view of the geometry of the set of its trajectories. (scholarpedia.org)
  • more generally, we look at the set of invariant measures of the associated dynamical system. (cnrs.fr)
  • In particular, I study statistical properties of dynamical systems related to recurrence, and connections to fractal geometry. (lu.se)
  • By using the closed-orbit theory including the effect of Coulomb scattering together with an electrical image potential approach, the recurrence spectra and the dynamical behaviours of the Rydberg hydrogen atom near a metal surface are presented. (epj.org)
  • During his doctorate in experimental psychology, which he completed in Trieste, Italy, Giuseppe studied applications of Dynamical Systems Theory in psychology and spent two years at the Center for Complex Systems at the Florida Atlantic University, USA. (leuphana.de)
  • The lecture will offer a self-contained introductory exposition of the theory of low-dimensional discrete dynamical systems. (cuni.cz)
  • One way to visualize the recurring nature of states by their trajectory through a phase space is the recurrence plot, introduced by Eckmann et al. (wikipedia.org)
  • However, making a recurrence plot enables us to investigate certain aspects of the m-dimensional phase space trajectory through a two-dimensional representation. (wikipedia.org)
  • The time-series corresponding to speech utterance is converted into complex network or graph using recurrence network approach to study the dynamical transitions. (amrita.edu)
  • Dynamical Diseases: Mathematical Analysis of Human Illness (American Institute of Physics, Woodbury, NY, 1995)], this Focus Issue offers an opportunity to reflect on the evolution of the field in traditional areas as well as contemporary data-based methods. (aip.org)
  • These methods are found to be significantly more effective at predicting coming large events than methods based on recurrence intervals. (scec.org)
  • The identified regimes as well as the set of dynamical variables explain large-scale weather patterns, which are associated, e.g., with severe winters over Eurasia and North America. (copernicus.org)
  • Complex Analysis and Dynamical Systems IV: Part 1. (maa.org)
  • Theoretical analysis and numerical simulation reveal that the impacts of the image potential contributing to the recurrence spectrum are qualitatively analogous to that of the parallel electrical and magnetic fields on the Rydberg atom. (epj.org)
  • The method combines the partitioning of recurrence networks and kernel principal component analysis. (copernicus.org)
  • We undertook a systematic review and individual patient data meta-analysis to investigate the efficacy and tolerability of different primaquine dosing regimens to prevent P vivax recurrence. (cdc.gov)
  • We assessed the effects of total dose and duration of primaquine regimens on the rate of first P vivax recurrence between day 7 and day 180 by Cox's proportional hazards regression (efficacy analysis). (cdc.gov)
  • Structural stability of dynamical systems was introduced in 1937, albeit with a different name, by Andronov and Pontrjagin in a short note (Andronov and Pontrjagin 1937). (scholarpedia.org)
  • The analogy with bifurcations in dynamical systems opens the possibility of mathematically modeling clinical conditions and investigating possible parameter changes that lead to avoidance of their pathological states. (aip.org)
  • In particular, we test the hypothesis that many shorter catalogs are as effective as one long catalog in determining algorithm parameters, and we find that the hypothesis is valid for the model when the catalogs are of the order of the mean recurrence interval. (scec.org)
  • The concept of Dynamical Diseases provides a framework to understand physiological control systems in pathological states due to their operating in an abnormal range of control parameters: this allows for the possibility of a return to normal condition by a redress of the values of the governing parameters. (aip.org)
  • This idea was closely associated with the mathematical concept of bifurcations that can occur in dynamical systems as certain parameters are changed. (aip.org)
  • Note: This paper is part of the Focus Issue on Dynamical Disease: A Translational Perspective. (aip.org)
  • It enables the detection of significant regimes of variability in addition to obtaining dynamical variables which can be used for regimes embedding. (copernicus.org)
  • The recurrence of states in nature has been known for a long time and has also been discussed in early work (e.g. (wikipedia.org)
  • The recurrence plot visualises R {\displaystyle \mathbf {R} } with coloured (mostly black) dot at coordinates ( i , j ) {\displaystyle (i,j)} if R ( i , j ) = 1 {\displaystyle R(i,j)=1} , with time at the x {\displaystyle x} - and y {\displaystyle y} -axes. (wikipedia.org)
  • They show that the set of points that have not achieved exponential growth in the derivative or slow recurrence to the critical point at a given time decays exponentially, which thereby implies further statistical properties. (springer.com)
  • We study the localization along a filter of several dynamical notions. (albany.edu)
  • In fact, we can deal with multiple constraints of the same form, and optimize pressure $h(\sigma,\mu) + \int A \,d\mu$ of yet another function $A$, and we can deal with more general dynamical systems (we mostly need a spectral gap for the Ruelle operator). (mathoverflow.net)