Studies On The Global Attractive And Positive Invariant Nature And Synchronization Of A Class Of Chaotic Systems

This paper mainly focuses on some character and the chaos synchronization of a class of nonlinear dynamical systems. Synchronization is one of these simplest dynamical actions of coupled systems. The main content is depicted as follows:First, in the third chapter we study the global attractive set and positive invariant set in the system: We think the controlled Lorenz system. The sense of the Jacobin matrix and the definition of the balanced point are used and the control term of the system.is given. Then by generalized Lyapunov function family, these methods and results of the global attractive set and positive invariant set of the system are delivered. The stability of the system is studied, and use these ellipsoid formulas are predigested by the system. So Leonov formula was proved. Some estimable formulas are put in one formula. The new formula will derive a group of other estimable formulas. Then, by the thought of intersection in geometry theory, these better results of the global attractive set and positive invariant set are obtained. With these results and methods, we may affirm that there isnot the balanced point of the system and periodic solution.Then, the linear feedback to conduct two chaotic systems is introduced. By these stability criterions of the noline system, the zero point of synchronous errors is progressive stabilization. Graphs of synchronous errors are given out the numerical value emulation s in the Matlab. These results indicate that the mater system and the slave system achieve synchronization quickly. Finally, this part investigates the synchronization of two new chaotic systems. A new sufficient condition of global asymptotic synchronization is attained from the theory of stability of time-varying systems. In addition, compared with thepreviously proposed method, the sufficient condition for the synchronization of two new chaotic systems issimpler and less conservative, and the range of coupled coefficients is wider. Numerical simulation shows the effectiveness and feasibility of this method.