Synchronization Between Integer-order Chaotic Systems and a Class of Fractional-order Chaotic Systems via Sliding Mode Control

Diyi Chen,1,a) Runfan Zhang,1 J. C. Sprott,2 Haitao Chen,1 and Xiaoyi Ma1,b)
1Department of Electrical Engineering, Northwest A&F University, Yangling, Shaanxi 712100,
People’s Republic of China
2Department of Physics, University of Wisconsin, Madison, Wisconsin 53706, USA

(Received 7 December 2011; accepted 8 May 2012; published online 29 May 2012)

ABSTRACT

In this paper, we focus on the synchronization between integer-order chaotic systems and a class of fractional-order chaotic system using the stability theory of fractional-order systems. A new sliding mode method is proposed to accomplish this end for different initial conditions and number of dimensions. More importantly, the vector controller is one-dimensional less than the system. Furthermore, three examples are presented to illustrate the effectiveness of the proposed scheme, which are the synchronization between a fractional-order Chen chaotic system and an integer-order T chaotic system, the synchronization between a fractional-order hyperchaotic system based on Chen’s system and an integer-order hyperchaotic system, and the synchronization between a fractional-order hyperchaotic system based on Chen’s system and an integer-order Lorenz chaotic system. Finally, numerical results are presented and are in agreement with theoretical analysis.

Ref: D. Chen, R. Zhang, J. C. Sprott, H. Chen, and X. Ma, Chaos 22, 023130-1 - 0123130-9 (2012)

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