Noisy Zhang-Dynamics (ZD) Method for Genesio Chaotic (GC) System Synchronization: Elegant Analyses and Unequal-Parameter Extension

Abstract

This paper handles the noise-free or noisy synchronization control of Genesio chaotic (GC) system. To do so, Zhang dynamics (ZD) method is presented and exploited, and thus the ZD controllers, noise-free or noisy, are theoretically researched. Firstly, the presented ZD controller for GC system synchronization with no noise perturbation is analyzed, and the synchronization error as a whole (i.e., in the form of vector norm) between the drive GC system and the response GC system converges globally exponentially to zero. Secondly, the presented ZD controller for GC system synchronization with noise perturbation is analyzed as well, and detailed theoretical analyses (i.e., proofs) and results show that the synchronization error as a whole (i.e., in the form of vector norm) converges globally to a small bound of error. So, the ZD controllers provided in this paper (including the ones with unequal parameters) are not only simple and effective but also quite robust for the GC system synchronization.