Simulative And Experimental Study On Synchronizing Chaotic And Fractional-order Chaotic Systems

Although the phenomenon of chaos is derived from the deterministic nonlinear system, its dynamical performance is pseudo-random. Chaos is characterized by a sensitive dependence of a system's dynamical variables on the initial conditions .For a long time past, it is generally considered that the chaos is a harmful phenomenon, so it is often desired to be avoided in many practical fields. However, the applying chaos has been one of the new and challenging project in nonlinear dynamical field since the chaos control and synchronization are proposed creatively. In recent year, the application of the chaos synchronization has been given much attention, by far some synchronization techniques have been used in many fields and progress has been made.The study on fractional-order calculus theory has a history more than 300 years. However, the applications of fractional calculus to physics and engineering are just a recent focus of interest. Many systems are known to display fractional order dynamics. The synchronization control of fractional-order system is the focus of recent researches, but chaotic synchronization methods are limited and few of fractional-order chaotic synchronization by circuit was reported. It is believed that the chaos synchronization will play an important role in fields such as secure communication in the future.In this paper, we have studied adaptive synchronization of chaotic and fractional-order chaotic systems using the numerical simulation and circuit simulation methods. The main contents can be divided into four parts. The first part gives the introduction of the predecessors'works systematically in this field including the notion, the methods and the application to practice of the chaos synchronization. In the second part, the numerical simulation and circuit simulation methods for synchronizing chaotic and fractional-order chaotic systems are given. In the third part, using adaptive synchronization control approach, based on Lyapunov stability theory, the synchronization and generalized projective synchronization methods for chaotic systems with uncertain parameters are studied. Adaptive controller and update law of parameters are obtained; the controller is simple and systemic. R osslerchaotic system, new three-dimensional autonomous chaos system, hyperchaotic Chen system, Chen chaotic system, hyperchaotic Lorenz system and Arneodo chaotic system are taken as examples to illustrate the effectiveness of proposed method. In the last part, using stability theory of fractional-order linear systems, a novel method of chaotic synchronization based on linearization by feedback is proposed for the fractional-order chaotic systems. The controller is obtained, and the method can be applied to solve synchronization problems of several classes of fractional-order chaotic systems, e.g., Lorenz system, R osslersystem, Chen system, Liu system, Lüsystem, R ossler and new hyperchaotic system. Numerical simulation and circuit simulation results are presented to demonstrate the effectiveness and feasibility of the proposed method.In general, we presented adaptive synchronization and generalized projective synchroni- zation methods for chaotic systems with uncertain parameters, and proposed a novel method of chaotic synchronization based on linearization by feedback for the fractional-order chaotic systems. Both numerical simulation and circuit simulation results are presented to demonstrate the effectiveness and feasibility. In fields on chaos synchronization research there are a few methods the same as the opinion of this paper, so they are not only the perfect complement to chaos synchronization and fractional-order chaotic synchronization thory, but also a profitable exploration to circuit for fractional-order chaotic synchronization in practice.