Control and synchronization of fractional-order chaotic systems


The chaotic dynamics of fractional-order systems and their applications in secure communication have gained the attention of many recent researches. Fractional-order systems provide extra degrees of freedom and control capability with integer-order differential equations as special cases. Synchronization is a necessary function in any communication system and is rather hard to be achieved for chaotic signals that are ideally aperiodic. This chapter provides a general scheme of control, switching and generalized synchronization of fractional-order chaotic systems. Several systems are used as examples for demonstrating the required mathematical analysis and simulation results validating it. The non-standard finite difference method, which is suitable for fractional-order chaotic systems, is used to solve each system and get the responses. Effect of the fractional-order parameter on the responses of the systems extended to fractional-order domain is considered. A control and switching synchronization technique is proposed that uses switching parameters to decide the role of each system as a master or slave. A generalized scheme for synchronizing a fractional-order chaotic system with another one or with a linear combination of two other fractional-order chaotic systems is presented. Static (timeindependent) and dynamic (time-dependent) synchronization, which could generate multiple scaled versions of the response, are discussed. © Springer International Publishing AG 2017.


Radwan A.G., Sayed W.S., Abd-El-Hafiz S.K.


Active nonlinear control; Amplitude modulation; Hidden attractors; Lyapunov stability; Non-standard finite difference schemes; Static and dynamic synchronization

Document Type



Studies in Computational Intelligence, Vol. 688, PP. 325 to 355, Doi: 10.1007/978-3-319-50249-6_11

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