Dual synchronization of chaotic and hyperchaotic systems

The existence of the dual synchronization behavior between a pair of chaotic and hyperchaotic systems is investigated via a nonlinear controller, in which the nonlinear functions of the system are used as a nonlinear feedback term. The sufficient conditions for achieving the dual synchronization behavior between a pair of chaotic and hyperchaotic systems using a nonlinear feedback controller are derived by using the Lyapunov stability theorem. The dual synchronization behavior between a pair of chaotic systems (Chen and Lorenz system) and a pair of hyperchaotic systems hyperchaotic Chen system and hyperchaotic Lu system are taken as two illustrative examples to show the effectiveness of the proposed method. Theoretical analysis and numerical simulations are performed to verify the results.