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Generalized finite-time synchronization between coupled chaotic systems of different orders with unknown parameters

Abstract

This letter investigates the adaptive finite-time synchronization of different coupled chaotic (or hyperchaotic) systems with unknown parameters. The sufficient conditions for achieving the generalized finite-time synchronization of two chaotic systems are derived based on the theory of finite-time stability of dynamical systems. By the adaptive control technique, the control laws and the corresponding parameters update laws are proposed such that the generalized finite-time synchronization of nonidentical chaotic (or hyperchaotic) systems is to be obtained. These results obtained are in good agreement with the existing one in open literature and it is shown that the technique introduced here can be further applied to various finite-time synchronizations between dynamical systems. Finally, numerical simulations are given to demonstrate the effectiveness of the proposed scheme.

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Acknowledgements

This work was supported by the China Postdoctoral Science Foundation funded project (No. 2013M532030) and the Natural Science Foundation of China (NSFC) under Grant 11272242.

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Correspondence to Jiakun Zhao.

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Zhao, J., Wu, Y. & Wang, Y. Generalized finite-time synchronization between coupled chaotic systems of different orders with unknown parameters. Nonlinear Dyn 74, 479–485 (2013). https://doi.org/10.1007/s11071-013-0970-0

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Keywords

  • Finite-time synchronization
  • Adaptive control
  • Hyperchaotic system
  • Unknown parameter