Application of Takagi-Sugeno Fuzzy Model to a Class of Chaotic Synchronization and Anti-synchronization

Diyi Chen, Weili Zhao, Julien Clinton Sprott & Xiaoyi Ma

Department of Electrical Engineering, Northwest A&F University, Shaanxi, Yangling 712100, P.R. China
Department of Physics, University of Wisconsin-Madison,
Madison, WI 53706, USA

Received: 31 January 2013 / Accepted: 23 March 2013 / Published online: 6 April 2013


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 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.

Ref: D. Chen, W. Zhao, J. C. Sprott, and X. Ma, Nonlinear Dynamics 73, 1495-1505 (2013)

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