A new approach to synchronization between two different chaotic systems with parametric perturbation

Abstract

The problem of chaotic synchronization between two different chaotic systems with parametric perturbation is studied. Based on Lyapunov stability law and norm theory，a sufficient condition to synchronize two different chaotic systems with parametric perturbation is given and a general way of choosing the controller is proposed. This method can realize the synchronization of two chaotic systems with parametric perturbation if the dimensions of the chaotic systems are equal and the state variables are measurable. And it is required that the control must decay to zero together with the errors as soon as the synchronization is reached. The proposed method is robust and can be used widely. Numerical simulations of synchronization between two chaotic systems，and synchronization between two hyperchaotic systems are provided to show the effectiveness and feasibility of the method.