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Control of finite-time anti-synchronization for variable-order fractional chaotic systems with unknown parameters

Abstract

Fractional-order chaotic system with variable-order and unknown parameters, as an excellent tool to describe the memory and hereditary characteristics of the complex phenomena in reality, remains important, but nowadays there exist few results about this system. This paper presents a finite-time anti-synchronization of two these systems based on the Mittag-Leffler stable theory and norm theory, in which the order varies with time and the unknown parameters of the systems are estimated. Moreover, a corollary about the monotone effect of variable order on the norm of the error system is deduced. We take different nonlinear variable orders for two identical Lü fractional chaotic systems and for two different Lü and Chen–Lee fractional chaotic systems as examples. The simulations illustrate the effectiveness and feasibility of the proposed control scheme.

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Acknowledgments

The authors are very grateful to editors and referees for valuable suggestions. This work is supported by the Foundation for the China Postdoctoral Science Foundation funded project (No. 2015M572033), the Foundation for the National Natural Science Foundation of China (No. 61273088; No. 61533011), Social Science Planning Fund Program of Shandong Province (No. 15CJJJ34) and development of Shandong University of Political Science and Law (No.2015Z01B).

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Correspondence to Li Zhang.

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Zhang, L., Yu, C. & Liu, T. Control of finite-time anti-synchronization for variable-order fractional chaotic systems with unknown parameters. Nonlinear Dyn 86, 1967–1980 (2016). https://doi.org/10.1007/s11071-016-3008-6

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Keywords

  • Fractional chaotic system
  • Anti-synchronization
  • Variable-order
  • Unknown parameters