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)
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.
The complete paper is available
in PDF format.
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