Synchronization between Integer-order Chaotic Systems and a
Class of Fractional-order Chaotic System based on Fuzzy Sliding
Mode Control
Diyi Chen, Shutang Liu
Department of Electrical Engineering, Northwest A&F
University, Yangling Shaanxi 712100, P.R. China
Julien Clinton Sprott
Department of Physics, University of Wisconsin,
Madison, WI 53706, USA
Xiaoyi Ma
Department of Electrical Engineering, Northwest A&F
University, Yangling Shaanxi 712100, P.R. China
Received: 30 April 2012 / Accepted: 24 July 2012 / Published
online: 11 August 2012
ABSTRACT
In this paper, we focus on the synchronization between
integer-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.