Synchronizing Genesio Chaotic System by Zhang-Dynamics Controller without or with Noise Perturbation

This paper investigates the synchronization control of Genesio chaotic system. For solving the synchronization problem of Genesio chaotic system, Zhang dynamics (ZD) method is firstly presented and utilized, and the corresponding ZD controller is designed and investigated for synchronizing control. On the one hand, the ZD controller for the synchronization of Genesio chaotic system without noise perturbation is considered, and the synchronization error between the drive Genesio chaotic subsystem and the response Genesio chaotic subsystem globally exponentially converges to zero. On the other hand, the ZD controller for the synchronization of Genesio chaotic system with noise perturbation is also considered, and detailed theoretical analyses show that the synchronization error globally converges to a small error bound or its inside. Note that the ZD controller provided here is not only effective but also robust for the synchronization of Genesio chaotic system. Finally, the simulations and comparisons with different methods for synchronizing Genesio chaotic system substantiate the efficacy, robustness and advantage of the presented ZD controller in the synchronization control.