Synchronization between fractional-order chaotic system and chaotic system of integer orders

Abstract

Based on the idea of tracking control and the stability theory of linear fractional-order system, chaotic synchronization between fractional-order chaotic system and chaotic system of integer orders is proposed. A compensation controller and a feedback controller are given. Synchronization between the fractional-order Chen chaotic system and the Loren chaotic system of integer orders is used to illustrate the effectiveness of the proposed synchronization approach. Numerical and circuit simulations coincide with the theoretical analysis.

Backstepping-based lag synchronization of a complex permanent magnet synchronous motor system

“…On the other hand, synchronization of fractional systems or synchronization of a fractional system and integer system, which shows fractional order has an influence on the synchronization, also attracts a lot of attention. For instance, the literature [12] reports the synchronization between a fractional system and integer system and the function projective synchronization was studied in Ref. [13].…”

A general method for synchronizing an integer-order chaotic system and a fractional-order chaotic system

“…It was found that in such a case synchronization can also be achieved. Zhou et al [15,16] first studied the synchronization be-tween a fractional-order system and an integer-order system. Based on the concept of tracking control, effective controllers were designed in Refs.…”

“…Based on the concept of tracking control, effective controllers were designed in Refs. [15] and [16] to achieve the synchronization. Later, via similar methods, they further studied the function projective synchronization between an integer-order Lorenz system and a fractional-order Chen system.…”

“…[19], though somewhat simpler than those in Refs. [15] and [16], has some drawbacks. One of them that should be mentioned is that the synchronization error in Ref.…”

Circuit Implementations, Bifurcations and Chaos of a Novel Fractional-Order Dynamical System

“…Furthermore, the chaotic synchronization between a fractional-order Chen chaotic system and an integerorder Lorenz chaotic system was investigated and its circuit simulation was carried out. [11] A kind of dislocated projective synchronization for Chua's fractionalorder system was successfully studied through a nonlinear controller in Ref. [12].…”