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

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.