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This paper presents a novel unified hyperchaotic system that contains the hyperchaotic Lorenz system and the hyperchaotic Chen system as two dual systems at the two extremes of its parameter spectrum. The new system is hyperchaotic over almost the whole range of the system parameter and continuously transfers from the hyperchaotic Lorenz system to the hyperchaotic Chen system. The new findings are not only demonstrated by computer simulations but also verified with bifurcation analysis, Lyapunov exponents and Lyapunov dimension.

In this paper, active control and adaptive control methods are applied, respectively. Adaptive control method is implemented when system parameters are unknown and active control method is applied when system parameters are known. Based on the Lyapunov stability theory, the controllers are designed to realize anti-synchronization, meanwhile, the update laws of parameters are proposed. The theoretical proof is given. And two groups of examples are shown to verify the effectiveness of the proposed schemes.