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Application of Takagi–Sugeno fuzzy model to a class of chaotic synchronization and anti-synchronization

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Abstract

In this study, we investigate a class of chaotic synchronization and anti-synchronization with stochastic parameters. A controller is composed of a compensation controller and a fuzzy controller which is designed based on fractional stability theory. Three typical examples, including the synchronization between an integer-order Chen system and a fractional-order Lü system, the anti-synchronization of different 4D fractional-order hyperchaotic systems with non-identical orders, and the synchronization between a 3D integer-order chaotic system and a 4D fractional-order hyperchaos system, are presented to illustrate the effectiveness of the controller. The numerical simulation results and theoretical analysis both demonstrate the effectiveness of the proposed approach. Overall, this study presents new insights concerning the concepts of synchronization and anti-synchronization, synchronization and control, the relationship of fractional and integer order nonlinear systems.

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Acknowledgements

This wok was supported by the scientific research foundation of National Natural Science Foundation (51109180), the National Science & Technology Supporting Plan from the Ministry of Science & Technology of China (2011BAD29B08) and the “111” Project from the Ministry of Education of P. R. of China and the State Administration of Foreign Experts Affairs of P.R. of China (B12007).

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Authors and Affiliations

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

    Diyi Chen, Weili Zhao & Xiaoyi Ma

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

    Julien Clinton Sprott

Authors
  1. Diyi Chen
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  2. Weili Zhao
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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., Zhao, W., Sprott, J.C. et al. Application of Takagi–Sugeno fuzzy model to a class of chaotic synchronization and anti-synchronization. Nonlinear Dyn 73, 1495–1505 (2013). https://doi.org/10.1007/s11071-013-0880-1

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  • DOI: https://doi.org/10.1007/s11071-013-0880-1

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