Abstract
The synchronization between fractional-order hyperchaotic systems and integer-order hyperchaotic systems via sliding mode controller is investigated. By designing an active sliding mode controller and choosing proper control parameters, the drive and response systems are synchronized. Synchronization between the fractional-order Chen chaotic system and the integer-order Chen chaotic system and between integer-order hyperchaotic Chen system and fractional-order hyperchaotic Rössler system is used to illustrate the effectiveness of the proposed synchronization approach. Numerical simulations coincide with the theoretical analysis.
Highlights
Fractional calculus has become a powerful tool to describe the dynamics of complex systems such as power systems, mathematics, biology, medicine, secure communication, and chemical reactors [1,2,3,4,5,6]
Chaos synchronization has attracted lots of attention in a variety of research fields [7,8,9,10,11,12,13] over the last two decades, because it can be applied in vast areas of physics and engineering and secure communication [14, 15]
Replacing for w(t) in (7) from w(t) of (13), the error dynamics on the sliding surface are determined by the following relation: De = (I − K(CK)−1C) Be
Summary
Fractional calculus has become a powerful tool to describe the dynamics of complex systems such as power systems, mathematics, biology, medicine, secure communication, and chemical reactors [1,2,3,4,5,6]. The problem of chaos synchronization between two different chaotic systems with fully unknown parameters is investigated in [18]. Chen and his partners [19] investigate the chaos control of a class of fractional-order chaotic systems via sliding mode. There is little information about the synchronization between fractionalorder chaotic systems and integer-order chaotic systems [20, 21]. The study of synchronization between fractional-order hyperchaotic systems and integer-order hyperchaotic systems is limited. Motivated by the above discussion, this paper investigates a sliding mode method for synchronization between a class of fractional-order hyperchaotic systems and integer-order hyperchaotic systems. The integer-order hyperchaotic systems are regarded as response system in the proposed synchronous technique which is simple and theoretically rigorous
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