Synchronization of systems of Marcus canonical equations driven by αα-stable noises

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 Lévy noise is considered. After discussing cocycle property, stationary orbits and random attractors, a synchronization phenomenon is shown to occur, when the drift terms of the coupled system satisfy certain dissipativity conditions. The synchronization result implies that coupled dynamical systems share a dynamical feature in certain asymptotic sense.