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Synchronization of two chaotic systems with three or two inputs via ZG method

Recently, the synchronization of two chaotic systems is attracting more and more attentions because of its potential applications in communication security, aerospace industry and many other fields. In this paper, by combining Zhang dynamics (ZD) and gradient dynamics (GD), a novel effective controller-design method termed Zhang-gradient (ZG) method is firstly developed for the chaos synchronization problem with multiple inputs (i.e., three or two inputs). Via this ZG method, the traditional three-input chaos synchronization problem can be successfully solved with desirable convergence rate and satisfactory accuracy. In addition, by taking advantage of the coupling property of the chaotic system, a creative extension of the ZG method is investigated to solve the thorny two-input chaos synchronization problem. Simulation verifications further demonstrate that the controllers based on the ZG method can not only achieve satisfactory synchronization accuracy and exponential convergence rate on the three-input chaos synchronization problem but also successfully solve the chaos synchronization problem with only two inputs.