Related papers: Numerical test for hyperbolicity of chaotic dynami…
Homoclinic chaos is usually examined with the hypothesis of hyperbolicity of the critical point. We consider here, following a (suitably adjusted) classical analytic method, the case of non-hyperbolic points and show that, under a…
The data generated by long-delayed dynamical systems can be organized in patterns by means of the so-called spatio-temporal representation, uncovering the role of multiple time-scales as independent degrees of freedom. However, their…
We show that the occurrence of chaotic diffusion in a typical class of time-delayed systems with linear instantaneous and nonlinear delayed term can be well described by an anti-persistent random walk. We numerically investigate the…
Inspired by the observation of a distributed time delay in the nonlinear response of an optical resonator, we investigate the effects of a similar delay on a noise-driven mechanical oscillator. For a delay time that is commensurate with the…
The mathematical - numerical analysis of a discrete dynamical model with two independent delays was performed. Such model may describe a continuous system with delays that have real rational number values. Applicable characteristic…
Impulsive control is used to suppress the chaotic behavior in an one-dimensional discrete supply and demand dynamical system. By perturbing periodically the state variable with constant impulses, the chaos can be suppressed. It is proved…
We consider a test problem for Navier-Stokes solvers based on the flow around a cylinder that exhibits chaotic behavior, to examine the behavior of various numerical methods. We choose a range of Reynolds numbers for which the flow is…
Collaboration between interconnected cyber-physical systems is becoming increasingly pervasive. Time-delays in communication channels between such systems are known to induce catastrophic failure modes, like high frequency oscillations in…
This paper presents a rigorous analytical model of traffic dynamics on a circular track, demonstrating the emergence of standing oscillations resulting from microscopic driver behaviour, delay responses, and proximity pressure. Without…
The problem of dynamic estimation of all parameters of a model representing chaotic and hyperchaotic systems using information from a scalar measured output is solved. The variational calculus based method is robust in the presence of…
This paper is the second in a series of two, and describes the current state of the art in modelling and prediction of chaotic time series. Sampled data from deterministic non-linear systems may look stochastic when analysed with linear…
We derive sufficient conditions for the solvability of the state estimation problem for a class of nonlinear control time-varying systems which includes those, whose dynamics have triangular structure. The state estimation is exhibited by…
In this article we study networks of coupled dynamical systems with time-delayed connections. If two such networks hold different delays on the connections it is in general possible that they exhibit different dynamical behavior as well. We…
We study the statistical properties of the time delay matrix $Q$ in the context of quantum transport through a chaotic cavity, in the absence of time-reversal invariance. First, we approach the problem from the point of view of random…
While invariant measures are widely employed to analyze physical systems when a direct study of pointwise trajectories is intractable, e.g., due to chaos or noise, they cannot uniquely identify the underlying dynamics. Our first result…
Systems with delayed feedback can possess chaotic attractors with extremely high dimension, even if only a few physical degrees of freedom are involved. We propose a state space reconstruction from time series data of a scalar observable,…
Numerical study of the parametric motion of energy levels in a model system built on Random Matrix Theory is presented. The correlation function of levels' slopes (the so called velocity correlation function) is determined numerically and…
Time delays may cause dramatic changes to the dynamics of interacting oscillators. Coupled networks of interacting dynamical systems can behave unexpectedly when the signal between the vertices are time delayed. It has been shown for a very…
In this article, on the example of the known low-order dynamical models, namely Lorenz, Rossler and Vallis systems, the difficulties of reliable numerical analysis of chaotic dynamical systems are discussed. For the Lorenz system, the…
The analysis of chaotic signals with time-frequency methods is considered. For this purpose, two new transformations are presented which consist in the decomposition of a signal onto an orthogonal set of respectively linear and hyperbolic…