Adaptive synchronization of different dimensional chaotic systems with unknown parameters

This work presents the adaptive synchronization between two different order chaotic systems with unknown parameters. Based on Lyapunov stability theory, a novel adaptive control law and a parameter update rule for unknown parameters are proposed. The proposed scheme can successfully synchronize some typical chaotic systems, such as the hyperchaotic Chen system and the Duffing equation. Numerical Simulation results verify the proposed schemepsilas effectiveness. Furthermore, the estimated values of the parameters are not identical to the real values under our discussions.