THE EFFECT OF FRACTIONAL ORDER ON SYNCHRONIZATION OF TWO FRACTIONAL ORDER CHAOTIC AND HYPERCHAOTIC SYSTEMS

This paper studies the synchronization of two commensurate fractional order chaotic and hyperchaotic systems using nonlinear control technique. We discuss some stability conditions of three and four dimensional fractional order systems. We apply these stability conditions to chaos and hyperchaos synchronization. The effect of fractional order on synchronization of fractional order chaotic and hyperchaotic systems is shown; chaos synchronization of the commensurate fractional order Liu system is achieved, while it is not achieved in its integer order counterparts using the same nonlinear controllers. Furthermore, achieving chaos synchronization via nonlinear control of the novel hyperchaotic system is found just in the fractional order case when using the same nonlinear control laws. Numerical simulations are used to verify the theoretical analysis.

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