Stabilization of a 5-D hyperchaotic Rikitake system with unknown parameters

Document Type : Research Article


School of Mechanical Engineering, Shiraz University, Shiraz, Islamic Republic of Iran


In this paper, a nonlinear 5-D hyperchaotic Rikitake dynamic system has been taken into consideration. The hyperchaotic behavior of the model was proved, and the response of the system has been shown. Besides, in the case of existing parametric uncertainties in the system, it shows even more complex behavior. An adaptive control strategy to have stable behavior is synchronized for an uncertain hyperchaotic system with an identical 5-D system. The stability of the control law has been identified by using the Lyapunov stability theory. The numerical simulations are presented for the hyperchaotic Rikitake system with unknown parameters and a system with time-varying parameters to indicate the effectiveness of the proposed algorithm for a class of complex systems. Moreover, since there are often lags between the signals gained by the system and the signals that the controller receives, the control input with the time delay parameter is implemented in the model. Also, the results show the gradual transformation from an unstable system into a stable one.


  • Phase portrait and time evolutions of the 5-D hyperchaotic Rikitake system is depicted.
  • Adaptive synchronization for autonomous and non-autonomous Rikitake model is proposed.
  • Time- delay existence  in control input is investigated.
  • Stability of the systems is guaranteed by the proposed strategy.


Main Subjects

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