Control And Synchronization On The Time-delayed Chaotic System

Researching the problems of dynamic system with time-delay is one of the leading edge topics in nonlinear dynamics domains. A time-delayed dynamic system can be able to portray the features more precisely and depict the essence of complexity of things. In this thesis, we discussed the phenomena of bifurcation, chaos control and their control techniques. The main contributions of the thesis are as following.1 Using the method of Taylor's and power's progression expanding, we analyze the corresponding transcendental characteristic equation and get the conditions of all equilibriums and Hopf bifurcation for this model. The difference of dissimilar time-delayed system and same time-delayed system is given.2 Upon the asymptotic stability of linear time-delayed system, a kind of nonlinear time-delayed system's stability is discussed. We get the control condition of the system's bifurcation by controlling time delay through the progression expanding analyze. Criteria are given to determine the stability and Hopf bifurcation.3 Nonlinear feedback control method and adaptive control method are suggested to control a class nonlinear time-delayed chaotic system. Under the condition of the parameters having error and no error, we get the criterion of the chaotic system controllable. Examples are given and numerical simulations are performed to illustrate the results.4 The synchronization of a class of unknown parameters time-delayed chaotic system is investigated and an adaptive control strategy is proposed. The asymptotic stability of synchronization is analyzed based on the Lyapunov theory, and the sufficient condition is obtained. Furthermore, the synchronization threshold of coupled system is estimated. According to this strategy, uncertain parameters are estimated. Using this control strategy, chaotic systems with the unknown parameters and the different initial conditions can be synchronized.5 We present a sliding mode control method for synchronizing a class of unknown parameters time-delayed chaotic system. The variable structure control...