International Journal of Stochastic Analysis
Volume 2010 (2010), Article ID 502803, 13 pages
doi:10.1155/2010/502803
Research Article

Synchronization of Dissipative Dynamical Systems Driven by Non-Gaussian Lévy Noises

Xianming Liu,1 Jinqiao Duan,1,2 Jicheng Liu,1 and Peter E. Kloeden3

1School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China
2Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616, USA
3Institut für Mathematik, Johann Wolfgang Goethe-Universität, D-60054, Frankfurt am Main, Germany

Received 17 September 2009; Accepted 15 January 2010

Academic Editor: Salah-Eldin Mohammed

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.

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 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.