Research on Synchronization of Bidirectional Coupled Chaotic Systems with Different Dimensions

This paper investigates the synchronization behavior in two bidirectional coupled chaotic financial systems with different dimensions. Firstly, using the generalized synchronization definition, scale matrix, direct design method and Lyapunov stability theory, the synchronization controller is designed for two different dimension systems. The dimension of two systems are controlled by selecting scale matrix. Secondly, the stability conditions is proposed by investigating the synchronization behavior of two chaotic systems. Finally, two examples are given to illustrate the effectiveness of the designed controllers.