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Synchronization between integer-order chaotic systems and a class of fractional-order chaotic system based on fuzzy sliding mode control

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Abstract

In this paper, we focus on the synchronization between integer-order chaotic systems and a class of fractional-order chaotic system using the stability theory of fractional-order systems. A new fuzzy sliding mode method is proposed to accomplish this end for different initial conditions and number of dimensions. Furthermore, three examples are presented to illustrate the effectiveness of the proposed scheme, which are the synchronization between a fractional-order Lü chaotic system and an integer-order Liu chaotic system, the synchronization between a fractional-order hyperchaotic system based on Chen’s system and an integer-order hyperchaotic system based upon the Lorenz system, and the synchronization between a fractional-order hyperchaotic system based on Chen’s system, and an integer-order Liu chaotic system. Finally, numerical results are presented and are in agreement with theoretical analysis.

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Acknowledgements

This wok was supported by the scientific research foundation of National Natural Science Foundation (51109180) and Personnel Special Fund of North West A&F University (RCZX-2009-01).

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Authors and Affiliations

  1. Department of Electrical Engineering, Northwest A&F University, Yangling, Shaanxi, 712100, P.R. China

    Diyi Chen, Runfan Zhang & Xiaoyi Ma

  2. Department of Physics, University of Wisconsin, Madison, WI, 53706, USA

    Julien Clinton Sprott

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  1. Diyi Chen
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  2. Runfan Zhang
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  3. Julien Clinton Sprott
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  4. Xiaoyi Ma
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Correspondence to Xiaoyi Ma.

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Chen, D., Zhang, R., Clinton Sprott, J. et al. Synchronization between integer-order chaotic systems and a class of fractional-order chaotic system based on fuzzy sliding mode control. Nonlinear Dyn 70, 1549–1561 (2012). https://doi.org/10.1007/s11071-012-0555-3

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