Projective synchronization in coupled integer and fractional order Liu-Chen chaotic systems

摘要

In this brief paper, projective synchronization (Projective Syn.) in coupled integer-order and fractional-order chaotic systems are both studied. For the case of driving coupled integer-order chaotic systems, theoretical analysis is carried out directly based on the Lyapunov stability theory. For the case of coupled fractional order chaotic system, we took a modified approximate method to obtain an equivalent integer order model for the fractional order chaotic system, which is much accurater than traditional approximation methods mentioned in literatures. Based on theoretical analysis, the mechanism of the occurrence of projective synchronization in coupled the fractional order chaotic systems is deduced in detailed. Also, a simple controller for adjusting the scaling factor of projective synchronization is designed, which can lead the states' evolution to desired value. This state error feedback controller is easily fulfilled in practice. Numerical experiments are also given to show the rightness of the theoretical analysis and the effectiveness of our proposed method by taking the newly proposed Liu-Chen system as an illustration.