Different Dimensional Chaotic Switching Circuit Design And Simulation Of Adaptive Synchronization

Recently, chaos control and synchronization have been an active research of the nonlinear subject. Hyperchaotic system has much more complex dynamical behavior, randomness, indeterminacy and so on. Now, Researcher focuses on chaos synchronization with different structures. Use kinds of ways to realize chaos synchronization.In order to meet the need of practical application, this paper designed a practical circuit of different dimension chaos system, and according to Adaptive controlling Theory, to realize chaos synchronization between chaotic systems with different dimension.This paper introduced two important definitions of chaos, several basic characters and methods in the research of chaos.First, a class of correlative three-dimensional chaotic and four-dimensional hyperchaotic switchable systems is built. Four-dimensional hyperchaotic system is designed bases on three-dimensional Lorenz system family. Some of its basic dynamical properties are studied in detail, such as the feature of equilibrium, the phase portraits of hyperchaotic attractor, the Lyapunov exponent and the fractal dimension. Furthermore, a practical circuit is designed to implement the switching between those6different systems, realized3kinds of chaotic systems and3kinds of hyperchaotic systemsFinial, to study a problem this is synchronization of chaotic systems with different dimension. In the case of unknown parameters and both derived systems, according to Lyapunov Stability Theory, and Adaptive controlling Theory, to realize chaos synchronization between chaotic systems with different dimensions. Taking Three-dimensional chaotic system and non-derived Four-dimensional hyperchaotic system as an example, based on the new Error function, to design an adaptive controller and a parameter adaptive law, realizing different dimensional synchronization of systems and to identify the unknown parameters. Numerical simulation shows the effectiveness and feasibility of the methods.The paper provided the switched circuit and the synchronization theory guide for the practical application of chaos system with different dimension. It has much instructive meaning in reality.