| The dynamic behavior and the problem of the control and synchronization of the single-mode traveling-wave lasers system,internal wave mechanics chaotic system and the lasers chaotic system are investigated in this paper.Firstly,the stability of the equilibrium points of three chaotic systems is analyzed simply,the dynamical behavior of each chaotic system when its parameters get certain values are discussed,the attractor diagram,bifurcation diagram,maximum Lyapunov exponent spectrum,Poincare section,power spectrum and return mapping are obtained by Matlab software.Secondly,The globally attractive set and positive invariant set of three chaotic systems are studied by constructing the positive definite and radial unbounded Lyapunov function.At the same time,the feedback controller is designed for three chaotic systems to realize the control of the unstable point or the only locally stable equilibrium positions.The second method of Lyapunov is used to discuss theoretically the rationality of the design of the controller.Finally,for three chaotic systems,the synchronization method of drive response is used,the sufficient conditions for global exponential synchronization of drive system and response system are obtained.And the numerical simulation by using Matlab software,the final simulation results show that the method is effective. |
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