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Synchronization of Fractional Hyperchaotic Rabinovich Systems via Linear and Nonlinear Control with an Application to Secure Communications

Adel Ouannas, Samir Bendoukha*, Christos Volos, Nouri Boumaza, and Abdulrahman Karouma
International Journal of Control, Automation, and Systems, vol. 17, no. 9, pp.2211-2219, 2019

Abstract : This paper proposes two approaches for the synchronization of a fractional hyperchaotic Rabinovich master-slave pair. The first approach introduces a linear control law to synchronize the systems in their ommensurate case, i.e. with a constant fractional-order. The convergence of the proposed scheme is proven by means of an appropriate Lyapunov functional. In the incommensurate scenario, a nonlinear controller is developed based on our choice of a suitable set of control parameters. Numerical results are presented to illustrate the validity and convergence of the proposed synchronization schemes. In addition, the incommensurate control law is applied to a signal-masking-based secure communication system, whose performance is assessed through simulations.

Keyword : "Commensurate and incommensurate systems, fractional hyperchaotic Rabinovich systems, fractional Laypunov method, linear and nonlinear controllers, secure chaotic communications."

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