Synchronization And Implementation Of Chaotic Systems With Constant LE Spectrum

The chaotic motion belongs to complex nonlinear movement, because chaos is sensitive to initial conditions, internal stochastic and continuous broad spectrum characteristics, which are widely used in physics, economics, biology, information science, social science and chemistry and other fields, such as signal and image encryption, secure communication. People pay more and more attention to the application of chaos theory. So the design and construction of a new chaotic system, chaos synchronization have become the key of chaos application.This paper mainly study on the problem of realization and synchronization of several kinds of chaotic systems with constant exponent spectrum. Based on the theoretical derivation and numerical simulation dynamic characteristics of this kind of systems are studied, and a variety of control methods are applied to implement the synchronization control. Finally circuit of the new proposed system and synchronization control scheme are realized with Multisim. The main contents of this dissertation are summarized as follows:1. Synchronization for a proposed chaotic system with constant Lyapunov exponent (LE) spectrum of is researched. First of all, the problem of chaos synchronization is changed into stability analysis of an error system. Then based on stability theory, four different kinds of synchronous controllers are designed to synchronize the master-slave systems and their gain expressions are given, through theoretical derivation and Lyapunov stability criterion to verify the feasibility of each controller. Finally, the impact of controller parameters for synchronous time is analyzed.2. A new chaotic system with constant LE spectrum is proposed based on Sprott system, which contains four parameters. The basic dynamic properties are studied and the LE spectrum and bifurcation diagram with respect to system parameters also are given for the proposed system. Three kinds of control methods are used to synchronize the new system. Finally the synchronous circuit simulation of the system is carried via Multisim software, which verified the implementation of the new system.3. The synchronization and parameter identification between the new system proposed in 2 and fractional order Chen system are illustrated. Based on the stability theory of fractional order and tracking control, a new method of synchronization and adaptive parameter learning algorithm is proposed, By means of numerical simulation and circuit simulation demonstrate the correctness and realization of the method.4. A new four-dimensional chaotic system is presented with two parameters constant LE spectrum. The constant LE spectral characteristics are analysed via LE spectrum and bifurcation diagram. An adaptive controller and parameter adaptive laws are designed through Lyapunov stability theory to realize the new system’s anti-synchronization. Through the numerical simulation verifies the validity of the scheme, and studied the effect of adjustable coefficient on anti-synchronization performance of the system. The last part of the circuit diagram of the adaptive anti-synchronization scheme is given, and the circuit simulation results agree with the numerical simulation.5. A new three-dimensional autonomous chaotic system with double parameters constant LE spectrum is presented. The dynamic properties of this new chaotic system are studied via attractor phase diagram, Poincare section, Lyapunov exponents, Lyapunov dimension and the signal power spectrum. The characteristics between system signals with parameters amplitude and phase inversion are researched, and verified via numerical simulation. We design a single controller to synchronize the new system with active feedback, adaptive method, back-stepping method and passive control method respectively, through theoretical derivation and numerical verification proves the correctness of the controller. Finally, in view of the above methods, a switching synchronization toolbox, combining of four methods, is designed to synchronize the new system via the combination of multiple switches.