Identification and synchronization of a 5-D hyperchaotic Rikitake system with unknown parameters

In this paper, a nonlinear 5-dimensional hyperchaotic Rikitake dynamic system and the uncontrolled response of the system has been taken into consideration. This system has hyper-chaotic behavior and in the case of existing uncertainties in the system, it shows even more complex behaviors. In order to have nonchaotic behavior, an adaptive control algorithm has been proposed to achieve synchronization for a hyperchaotic system with an identical 5-D system which has unknown parameters. The stability of the control law by using the Lyapunov stability theory system has been identified. For instance, to show the effectiveness of the proposed algorithm for a class of complex systems, the numerical simulation are presented for a hyperchaotic Rikitake system with unknown parameters. Also, the results depict that the gradual transformation from a chaotic system into a periodic one. Finally, the effectiveness of the proposed methodology has been adopted for the system with time-varying parameters. To the best of our knowledge, it is for the first time that adaptive synchronization for a 5-D hyperchaotic Rikitake system with uncertainty has been taken into account by our team.

Keywords:

Adaptive control , Chaos , Hyperchaos , Synchronization.