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Asymptotic theory of chaotic synchronization for dissipative-coupled dynamical systems

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  • Verichev, Nikolai N.
  • Verichev, Stanislav N.
  • Wiercigroch, Marian

Abstract

In this paper, a general asymptotic theory of synchronization of the chaotic oscillations for non-identical dissipative-coupled dynamical systems is proposed. The theory is based on the general definition of synchronization and on the method of integral manifolds. A number of different cases of non-identical dynamical systems and their couplings when the synchronization is asymptotically close to the identical one have been considered. This theory is mutually valid for the master and slave in synchronization of dynamical systems including the systems with slowly varying parameters. Theoretical findings are supported by the results of numerical simulation.

Suggested Citation

  • Verichev, Nikolai N. & Verichev, Stanislav N. & Wiercigroch, Marian, 2009. "Asymptotic theory of chaotic synchronization for dissipative-coupled dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 752-763.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:2:p:752-763
    DOI: 10.1016/j.chaos.2008.03.007
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    1. Andrzej Stefanski & Tomasz kapitaniak, 2000. "Using chaos synchronization to estimate the largest lyapunov exponent of nonsmooth systems," Discrete Dynamics in Nature and Society, Hindawi, vol. 4, pages 1-9, January.
    2. Yassen, M.T., 2005. "Controlling chaos and synchronization for new chaotic system using linear feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 913-920.
    3. Verichev, Nikolai N. & Verichev, Stanislav N. & Wiercigroch, Marian, 2007. "Physical interpretation and theory of existence of cluster structures in lattices of dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 34(4), pages 1082-1104.
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    1. Verichev, Nikolai N. & Verichev, Stanislav N. & Wiercigroch, Marian, 2009. "C-oscillators and stability of stationary cluster structures in lattices of diffusively coupled oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 686-701.

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