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Parameter mismatches, variable delay times and synchronization in time-delayed systems

Author

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  • Shahverdiev, E.M.
  • Nuriev, R.A.
  • Hashimov, R.H.
  • Shore, K.A.

Abstract

We investigate synchronization between two unidirectionally linearly coupled chaotic non-identical time-delayed systems and show that parameter mismatches are of crucial importance to achieve synchronization. We establish that independent of the relation between the delay time in the coupled systems and the coupling delay time, only retarded synchronization with the coupling delay time is obtained. We show that with parameter mismatch or without it neither complete nor anticipating synchronization occurs. We derive existence and stability conditions for the retarded synchronization manifold. We demonstrate our approach using examples of the Ikeda and Mackey Glass models. Also for the first time we investigate chaos synchronization in time-delayed systems with variable delay time and find both existence and sufficient stability conditions for the retarded synchronization manifold with the coupling-delay lag time. Also for the first time we consider synchronization between two unidirectionally coupled chaotic multi-feedback Ikeda systems and derive existence and stability conditions for the different anticipating, lag, and complete synchronization regimes.

Suggested Citation

  • Shahverdiev, E.M. & Nuriev, R.A. & Hashimov, R.H. & Shore, K.A., 2005. "Parameter mismatches, variable delay times and synchronization in time-delayed systems," Chaos, Solitons & Fractals, Elsevier, vol. 25(2), pages 325-331.
    • Handle: RePEc:eee:chsofr:v:25:y:2005:i:2:p:325-331
    DOI: 10.1016/j.chaos.2004.08.009
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    Cited by:

    1. Xu, Jian & Chung, Kwok-Wai, 2009. "Dynamics for a class of nonlinear systems with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 28-49.
    2. Hoang, Thang Manh, 2011. "Complex synchronization manifold in coupled time-delayed systems," Chaos, Solitons & Fractals, Elsevier, vol. 44(1), pages 48-57.
    3. Banerjee, Santo, 2009. "Synchronization of time-delayed systems with chaotic modulation and cryptography," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 745-750.
    4. Ge, Zheng-Ming & Yang, Kun-Wei, 2007. "Chaotic ranges of a unified chaotic system and its chaos for five periodic switch cases," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 246-269.
    5. Chen, Yen-Sheng & Chang, Chien-Cheng, 2009. "Impulsive synchronization of Lipschitz chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1221-1228.
    6. Shahverdiev, E.M. & Hashimova, L.H. & Hashimova, N.T., 2008. "Chaos synchronization in some power systems," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 827-834.

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