A Novel Hyperchaotic system, Control and synchronization

In this paper, a novel 4-D hyperchaotic system based on the memristor simplest chaotic circuit system (MSCC) is proposed. First, we recall some brief notions on the chaotic phenomenon which appears in a deterministic dynamic system. Next, the dynamic properties of the proposed system are investigated, including equilibrium points, Lyapunov exponents, dissipativity and Kaplan-Yorke dimension. Then, these novel hyper chaotic system has five equilibrium points and hence it exhibits a strange four-wing hyper chaotic attractor. In addition, an adaptive control to obtain the stability of the system is designed. Finally, the generalized synchronization between the novel hyper chaotic system and MSCC system via active control method is successfully achieved using stability theorem of linear systems. Simulation examples are also given to illustrate and validate the proposed control and synchronization methods.