Anti-synchronization of different hyperchaotic systems based on adaptive active control and fractional sliding mode control

Taking hyperchaotic Chen system and hyperchaotic Lorenz system as examples, we study the anti-synchronization of hyperchaotic systems with slow time-varying parameters. Firstly, taking advantage of active control concept, the non-linear parts of hyperchaotic systems are eliminated, and then based on Lyapunov stability theory, a kind of parameter adaptive control law is selected reasonably to achieve anti-synchronization of two hyperchaotic systems, which is a good solution to the time-varying parameters perturbation problem. Furthermore, hyperchaotic systems of different parameters with fractional order are studied via sliding mode control, which is proved to be valid theoretically. Numerical simulation experiments verify the effectiveness and feasibility of the proposed method.