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