Synchronization of dissipative dynamical systems driven by non-Gaussian Levy noises

TL;DR

This paper investigates how coupled dissipative dynamical systems driven by non-Gaussian Levy noises can synchronize, revealing that under certain conditions, they exhibit shared long-term behavior despite complex stochastic influences.

Contribution

It introduces the analysis of synchronization phenomena in coupled systems influenced by non-Gaussian Levy noises, extending understanding beyond Gaussian noise models.

Findings

Synchronization occurs under dissipativity and integrability conditions.

Coupled systems share asymptotic dynamical features.

Analysis includes cocycle property, stationary orbits, and random attractors.

Abstract

Dynamical systems driven by Gaussian noises have been considered extensively in modeling, simulation and theory. However, complex systems in engineering and science are often subject to non-Gaussian fluctuations or uncertainties. A coupled dynamical system under non- Gaussian Levy noises is considered. After discussing cocycle prop- erty, stationary orbits and random attractors, a synchronization phe- nomenon is shown to occur, when the drift terms of the coupled system satisfy certain dissipativity and integrability conditions. The synchro- nization result implies that coupled dynamical systems share a dy- namical feature in some asymptotic sense.