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Synchronization of dissipative dynamical systems driven by non-Gaussian Lévy noises. (English) Zbl 1218.60051

Summary: 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 the 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.

MSC:

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
37H10 Generation, random and stochastic difference and differential equations
60G51 Processes with independent increments; Lévy processes
93B52 Feedback control
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