Generalized Synchronization Between Chen System and Rucklidge System

This paper investigates the two problems of generalized chaotic synchronization. In one case, the Chen system is treated as the drive system and the controlled Rucklidge system as the response system. In the other case, we choose the Rucklidge system as the drive system and the controlled Chen system as the response system. For each case, a scalar control input and a state transformation are proposed by using the differential geometric approach when a simple condition holds. Under the scalar control input and the state transformation, the trajectory of the response system can track the trajectory of the drive system no matter what initial values of the two systems. The two generalized synchronizations realized in this paper reveal the Rucklidge system and the Chen system are similar in some sense although their system equations are quite different. Finally, several numerical simulations are studied to demonstrate the control schemes given in this paper.