相关论文: Lyapunov Instability versus Relaxation Time in two…

This article proposes an approach to construct a Lyapunov function for a linear coupled impulsive system consisting of two time-invariant subsystems. In contrast to various variants of small-gain stability conditions for coupled systems,…

We study chaotic behavior of order parameters in two coupled ensembles of self-sustained oscillators. Coupling within each of these ensembles is switched on and off alternately, while the mutual interaction between these two subsystems is…

This paper focuses on a fundamental inquiry in a coupled oscillator model framework. It specifically addresses the direction of net information flow in mutually coupled non-identical chaotic oscillators. Adopting a specific form of…

For general dissipative dynamical systems we study what fraction of solutions exhibit chaotic behavior depending on the dimensionality $d$ of the phase space. We find that a system of $d$ globally coupled ODE's with quadratic and cubic…

We describe a flexible and modular delayed-feedback nonlinear oscillator that is capable of generating a wide range of dynamical behaviours, from periodic oscillations to high-dimensional chaos. The oscillator uses electrooptic modulation…

We show that small perturbations in the boost-invariant color fields of the glasma exhibit an exponential growth with the square root of time. We interpret this growth rate as a Lyapunov exponent, related to entropy production and the…

Through molecular dynamics, we study the $d=2,3$ classical model of $N$ coupled rotators (inertial XY model) assuming a coupling constant which decays with distance as $r_{ij}^{-\alpha}$ ($\alpha \ge 0$). The total energy $<H>$ is…

The sensitive dependence of chaos on parameters is a topic of great interest in the study of integrability and stability of dynamical systems. Previous work has proposed ways to identify the sensitive dependence on parameters by topological…

In order to study the chaotic behavior of a system with non-local interactions, we will consider weakly coupled non-commutative field theories. We compute the Lyapunov exponent of this exponential growth in the large Moyal-scale limit to…

We compute Lyapunov vectors (LVs) corresponding to the largest Lyapunov exponents in delay-differential equations with large time delay. We find that characteristic LVs, and backward (Gram-Schmidt) LVs, exhibit long-range correlations,…

The dephasing time in coupled mesoscopic conductors is caused by the fluctuations of the dipolar charge permitted by the long range Coulomb interaction. We relate the phase breaking time to elementary transport coefficients which describe…

The Lyapunov spectrum describes the exponential growth, or decay, of infinitesimal phase-space perturbations. The perturbation associated with the maximum Lyapunov exponent is strongly localized in space, and only a small fraction of all…

The parametric instability contribution to the largest Lyapunov exponent (LLE) is derived for a mean-field Hamiltonian model, with attractive long-range interactions. This uses a recent Riemannian approach to describe Hamiltonian chaos with…

A mathematical model of autoresonance in nonlinear systems with combined parametric and external chirped frequency excitation is considered. Solutions with a growing amplitude and a bounded phase mismatch are associated with the…

An autonomous system of ordinary differential equations describing nonlinear oscillations on the plane is considered. The influence of time-dependent perturbations decaying at infinity in time is investigated. It is assumed that the…

We use a recent result to show that the rate of loss of coherence of a quantum system increases with increasing system phase space structure and that a chaotic quantal system in the semiclassical limit decoheres exponentially with rate $2…

Many real-world dynamics exhibit chaos, a phenomenon in which neighboring trajectories in the state space of a dynamical system diverge exponentially over time. A common measure used for quantifying the degree of this divergence is the…

We study systems with periodically oscillating parameters that can give way to complex periodic or non periodic orbits. Performing the long time limit, we can define ergodic averages such as Lyapunov exponents, where a negative maximal…

We consider relaxation processes that exhibit a stretched exponential behavior. We find that in those systems, where the relaxation arises from two competing exponential processes, the size of the system may play a dominant role. Above a…

In this paper we consider the problem of determining the stability properties, and in particular assessing the exponential stability, of a singularly perturbed linear switching system. One of the challenges of this problem arises from the…