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
and
Department of Physics, University of Wisconsin-Madison,
Madison, WI 53706, USA
Received: 31 January 2013 / Accepted: 23 March 2013 / Published
online: 6 April 2013
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 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)