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

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  • Xianming Liu
  • Jinqiao Duan
  • Jicheng Liu
  • Peter E. Kloeden

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.

Suggested Citation

  • Xianming Liu & Jinqiao Duan & Jicheng Liu & Peter E. Kloeden, 2010. "Synchronization of Dissipative Dynamical Systems Driven by Non-Gaussian Lévy Noises," International Journal of Stochastic Analysis, Hindawi, vol. 2010, pages 1-13, February.
    • Handle: RePEc:hin:jnijsa:502803
    DOI: 10.1155/2010/502803
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