Chaos Control And The Construction Of Time-Delayed Chaotic System And Its Application

We make researches on the theory and experiment for controlling Chen system and time-delayed system with notch filter feedback signal, forming simple time-delayed chaotic systems through hopf bifurcation analysis,the synchronization of time-delayed systems and the oscillating death in time-delayed system.With the theory and method of Hopf bifurcation, the condition of Hopf bifurcation, its direction and the stability for controlling the Chen system with notch filter feedback signal are analytically determined, but for time-delayed system we can only analyze the condition of Hopf bifurcation. With the condition we can control the chaotic system to periodic state. The circuit experiments and numerical simulations are done based on the controllable parameter values. The validity of theoretic analysis and the feasibility of this scheme to control chaotic system are well proved by the results.We propose to form simple time-delayed chaotic systems with only several nonlinear polynomials. In the whole forming processes, we follow the period doubling bifurcation route to chaos. Given some basic assumptions, we can analytically determine the conditions for a time-delayed system to have a limit cycle solution generated from Hopf bifurcation. The stability and bifurcating direction are also analyzed. Then the bifurcation parameter is changed along the Hopf bifurcating direction and the chaotic state is confirmed by calculating the largest Lyapunov exponent. Finally, we realize the formulated time-delayed chaotic systems in nonlinear electronic circuits. The analyzing results and numerical computations are consistent with nonlinear circuit experiments well.Furthermore we consider the synchronization both of the same and the different time-delayed systems and give the result of the circuit experiments.Finally the oscillating death in time-delayed system is investigated. We give the critical curve with numerical simulation and do the simulation based on it.The research in this paper provides theoretical foundation for chaos control. And the time-delayed systems also provide a good platform for the application of chaos.