Search results for "dynamical system"

Lyapunov quantities and limit cycles in two-dimensional dynamical systems : analytical methods, symbolic computation and visualization

2011

A hybrid stimulation strategy for suppression of spiral waves in cardiac tissue

2011

International audience; Atrial fibrillation (AF) is the most common cardiac arrhythmia whose mechanisms are thought to be mainly due to the self perpetuation of spiral waves (SW). To date, available treatment strategies (antiarrhythmic drugs, radiofrequency ablation of the substrate, electrical cardioversion) to restore and to maintain a normal sinus rhythm have limitations and are associated with AF recurrences. The aim of this study was to assess a way of suppressing SW by applying multifocal electrical stimulations in a simulated cardiac tissue using a 2D FitzHugh-Nagumo model specially convenient for AF investigations. We identified stimulation parameters for successful termination of S…

Recursion at the crossroads of sequence modeling, random trees, stochastic algorithms and martingales

2013

This monograph synthesizes several studies spanning from dynamical systems in the statistical analysis of sequences, to analysis of algorithms in random trees and discrete stochastic processes. These works find applications in various fields ranging from biological sequences to linear regression models, branching processes, through functional statistics and estimates of risk indicators for insurances. All the established results use, in one way or another, the recursive property of the structure under study, by highlighting invariants such as martingales, which are at the heart of this monograph, as tools as well as objects of study.

Introducing the DYNAMICS framework of moment-to-moment development in achievement motivation

2022

This article introduces a new theoretical and psychometric framework describing moment-to-moment development and inter-dependencies of achievement motivation in terms of the situated expectancy-value theory, by introducing dynamical systems concepts into this line of research. As a first empirical example of a study using this framework, we examined whether task values, costs, and success expectancies measured in a learning situation (time point t) predicted themselves and each other at the next situation (t + 1; 27 min later) within a weekly university lecture. Situational task values, expectancies, and costs were assessed using the experience sampling method in 155 university teacher trai…

Wiener-Granger Causality in Network Physiology with Applications to Cardiovascular Control and Neuroscience

2016

Since the operative definition given by C. W. J. Granger of an idea expressed by N. Wiener, the Wiener–Granger causality (WGC) has been one of the most relevant concepts exploited by modern time series analysis. Indeed, in networks formed by multiple components, working according to the notion of segregation and interacting with each other according to the principle of integration, inferring causality has opened a window on the effective connectivity of the network and has linked experimental evidences to functions and mechanisms. This tutorial reviews predictability improvement, information-based and frequency domain methods for inferring WGC among physiological processes from multivariate…

Quasiconformal Jordan Domains

2020

We extend the classical Carath\'eodory extension theorem to quasiconformal Jordan domains $( Y, d_{Y} )$. We say that a metric space $( Y, d_{Y} )$ is a quasiconformal Jordan domain if the completion $\overline{Y}$ of $( Y, d_{Y} )$ has finite Hausdorff $2$-measure, the boundary $\partial Y = \overline{Y} \setminus Y$ is homeomorphic to $\mathbb{S}^{1}$, and there exists a homeomorphism $\phi \colon \mathbb{D} \rightarrow ( Y, d_{Y} )$ that is quasiconformal in the geometric sense. We show that $\phi$ has a continuous, monotone, and surjective extension $\Phi \colon \overline{ \mathbb{D} } \rightarrow \overline{ Y }$. This result is best possible in this generality. In addition, we find a n…

Acoustic wave guides as infinite-dimensional dynamical systems

2015

We prove the unique solvability, passivity/conservativity and some regularity results of two mathematical models for acoustic wave propagation in curved, variable diameter tubular structures of finite length. The first of the models is the generalised Webster's model that includes dissipation and curvature of the 1D waveguide. The second model is the scattering passive, boundary controlled wave equation on 3D waveguides. The two models are treated in an unified fashion so that the results on the wave equation reduce to the corresponding results of approximating Webster's model at the limit of vanishing waveguide intersection.

Towards a global view of dynamical systems, for the C1-topology.

2010

This paper suggests a program for getting a global view of the dynamics of diffeomorphisms, from the point of view of the C1-topology. More precisely, given any compact manifold M, one splits Diff1(M) in disjoint C1-open regions whose union is C1-dense, and conjectures state that these open set, and their complement, are characterized by the presence of • either a robust local phenomenon • or a global structure forbiding this local phenomenon. Other conjectures states that some of these regions are empty. This set of conjectures draws a global view of the dynamics, putting in evidence the coherence of the numerous recent results on C1-generic dynamics.

Numerical methods for a nonlinear impact model: A comparative study with closed-form corrections

2011

A physically based impact model-already known and exploited in the field of sound synthesis-is studied using both analytical tools and numerical simulations. It is shown that the Hamiltonian of a physical system composed of a mass impacting on a wall can be expressed analytically as a function of the mass velocity during contact. Moreover, an efficient and accurate approximation for the mass outbound velocity is presented, which allows to estimate the Hamiltonian at the end of the contact. Analytical results are then compared to numerical simulations obtained by discretizing the system with several numerical methods. It is shown that, for some regions of the parameter space, the trajectorie…

Assessing Transfer Entropy in cardiovascular and respiratory time series: A VARFI approach

2021

In the study of complex biomedical systems represented by multivariate stochastic processes, such as the cardiovascular and respiratory systems, an issue of great relevance is the description of the system dynamics spanning multiple temporal scales. Recently, the quantification of multiscale complexity based on linear parametric models, incorporating autoregressive coefficients and fractional integration, encompassing short term dynamics and long-range correlations, was extended to multivariate time series. Within this Vector AutoRegressive Fractionally Integrated (VARFI) framework formalized for Gaussian processes, in this work we propose to estimate the Transfer Entropy, or equivalently G…