Adaptive modified synchronization of hyperchaotic systems with fully unknown parameters

In this paper, we demonstrate that the adaptive hybrid synchronization behavior can coexist in two identical and different hyperchaotic systems with terms of parametric uncertainty. By using rigorous mathematical theory, the controller is designed based on Lyapunov stability theory and an analytic expression of the controller with its adaptive laws of parameters is shown. The adaptive hybrid synchronization between two identical systems (hyperchaotic Lü system) and different systems (hyperchaotic Lorenz and hyperchaotic Chen systems) are taken as two illustrative examples to show the effectiveness of the proposed method. Theoretical analysis and numerical simulations are shown to verify the results. © 2014, Springer-Verlag Berlin Heidelberg.