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

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• 作者：Diyi Chen (1)
  Weili Zhao (1)
  Julien Clinton Sprott (2)
  Xiaoyi Ma (1)
  
• 关键词：Synchronization ; Anti ; synchronization ; Integer ; order chaotic system ; Fractional ; order chaotic system ; Takagi–Sugeno fuzzy
• 刊名：Nonlinear Dynamics
• 出版年：2013
• 出版时间：August 2013
• 年：2013
• 卷：73
• 期：3
• 页码：1495-1505
• 全文大小：579KB
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• 作者单位：Diyi Chen (1)
  Weili Zhao (1)
  Julien Clinton Sprott (2)
  Xiaoyi Ma (1)
  
  1. Department of Electrical Engineering, Northwest A&F University, Shaanxi, Yangling, 712100, P.R. China
  2. Department of Physics, University of Wisconsin, Madison, WI, 53706, USA
  

文摘

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.