Related papers: Numerical test for hyperbolicity of chaotic dynami…
A powerful tool is developed for the characterization of chaotic signals. The approach is based on the symbolic encoding of time series (according to their ordinal patterns) combined with the ensuing characterization of the corresponding…
The presence of chaotic transients in a nonlinear dynamo is investigated through numerical simulations of the 3D magnetohydrodynamic equations. By using the kinetic helicity of the flow as a control parameter, a hysteretic blowout…
We propose an example of smooth autonomous system governed by differential delay equation manifesting chaotic dynamics apparently associated with hyperbolic attractor of Smale - Williams type. The general idea is to depart from a system…
This paper deals with adaptive synchronization of chaos in the presence of time-varying communication-delays. We consider two bidirectionally coupled systems that seek to synchronize through a signal that each system sends to the other one…
From the climate system to the effect of the internet on society, chaotic systems appear to have a significant role in our future. Here a method of statistical learning for a class of chaotic systems is described along with underlying…
This article investigates the stability of pantograph delay differential equations, in which the delayed argument is proportional to the present time. We derive analytic criteria that partition the parameter plane into unstable,…
In this paper, we introduce the notion of distributional chaos and the measure of chaos for random dynamical systems generated by two interval maps. We give some sufficient conditions for a zero measure of chaos and examples of chaotic…
We present an inverse method to construct large classes of chaotic invariant sets together with their exact statistics. The associated dynamical systems are characterized by a probability distribution and a two-form. While our emphasis is…
Non-ideal deterministic system "tank with liquid-electric motor" is studied. Two delay-approximation models are considered. Impact of the delay on the emergence, evolution and disappearance of regular and chaotic limit sets (attractors) of…
We present the linear-stability analysis of synchronised states in coupled time-delay systems. There exists a synchronisation threshold, for which we derive upper bounds, which does not depend on the delay time. We prove that at least for…
We perform a detailed study of the chaotic component in mixed-type Hamiltonian systems on the example of a family of billiards [introduced by Robnik in J. Phys. A: Math. Gen. 16, 3971 (1983)]. The phase space is divided into a grid of cells…
We introduce "state space persistence analysis" for deducing the symbolic dynamics of time series data obtained from high-dimensional chaotic attractors. To this end, we adapt a topological data analysis technique known as persistent…
We discuss two mechanical systems with hyperbolic chaotic attractors of Smale - Williams type. Both models are based on Froude pendulums. The first system is composed of two coupled Froude pendulums with alternating periodic braking. The…
We analyze the decay of classically chaotic quantum systems in the presence of fast ballistic escape routes on the Ehrenfest time scale. For a continuous excitation process, the form factor of the decay cross section deviates from the…
The established thermodynamic formalism of chaotic dynamics, valid at statistical equilibrium, is here generalized to systems out of equilibrium, that have yet to relax to a steady state. A relation between information, escape rate, and the…
An experimental approach is taken to study the dynamics of the dripping water faucet, a simple deterministic system. The time interval between successive drops may be affected by the many drops preceding it. The time interval is predicted…
Systems with time-delayed chaotic dynamics are common in nature, from control theory to aeronautical propulsion. The overarching objective of this paper is to compute the stability properties of a chaotic dynamical system, which is…
We extend the mathematical model based on stochastic differential equations describing the error gained by an atomic clock to the cases of anomalous behavior including jumps and an increase of instability. We prove an exact iterative…
We study the validity of the Born-Oppenheimer approximation in chaotic dynamics. Using numerical solutions of autonomous Fermi accelerators, we show that the general adiabatic conditions can be interpreted as the narrowness of the chaotic…
We propose a measure of divergence of probability distributions for quantifying the dissimilarity of two chaotic attractors. This measure is defined in terms of a generalized entropy. We illustrate our procedure by considering the effect of…