The Method Of Controlling Chaos Theory And Its Electronic Circuit Of The Experimental Study

The paper researches on the control of chaos or hyperchaos via the method of the tune-delayed feedback control(DFC), the proportional periodic pulse perturbation to the system variables (PP-SV) and limiting amplitude. First, based on the arisen conditions of Hopf bifurcation of the delay system and the corresponding handling methods, we propose an analytic method for achieving the controlling conditions when a low-dimensional chaos system is controlled by DFC, and obtain the function relation of controlling parameters. The method has been applied to some examples and the circuit experiment and the results show that it is important to control chaotic systems. Second, we propose an enhancing project based on the practical application. Moreover, with the method of emerging Hopf bifurcation of the system, the analytic conditions that the low-dimension continuous autonomous chaotic systems controlled by the project are given in theory. Applying the conclusions we got to the practical systems, the method is shown by the theoretical description and numerical calculation that it is effective. Last, we have a elementary research on the foundational period of nonlinear autonomous systems. The method of PP-SV is improved according to the questions in controlling chaos and hyperchaos systems with it. The high-dimension continuous hyperchaos system and the discrete hyperchaos system are studied respectively with the method proposed. The control of hyperchaos in the circuit with the method of PP-SV is also realized in the paper. By the improved method, the experimental results accord with the numerical results. In addition, we design an experiment circuit for controlling hyperchaos via limiting amplitude. The circuit is implemented simply and the controlling phenomenon is obvious.Above the methods we discussed in the paper are all effective for the controlling chaos or hyperchaos, and instructive to the practical application.