Chaos synchronization of different chaotic systems subjected to input nonlinearity

In this paper, a unified mathematical expression describing a class of synchronization systems is presented, for which the problem of chaos synchronization between different chaotic systems with input nonlinearity has been studied. Based on Lyapunov stability theory, a sliding mode controller and some generic sufficient conditions for global asymptotic synchronization are designed such that the error dynamics of two different chaotic motions satisfy stability in the Lyapunov sense in spite of the input nonlinearity. This technique is applied to achieve chaos synchronization of three pairs of different chaotic systems (Lorenz–Chen, Chen–Liu, and Liu–Lorenz) in drive–response structure. The numerical simulation results demonstrate the validity and feasibility of the proposed controller.