Copyright © 2010 Xianming Liu et al. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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 a class of Lévy noises 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 and integrability conditions. The synchronization
result implies that coupled dynamical systems share a dynamical
feature in some asymptotic sense.