| Since the Lorenz discover the first chaos attractor, chaos theory has been obtained huge, far-reaching development in many fields. Chaos has far-ranging applied foreground in many fields such as biological engineering, electronic engineering, chemical engineering, information engineering, application mathematics and experimental physics and so on. Sometimes, the existence of chaos may improve the performance of system. Under such condition, generating chaos or enhancing existing chaos is referred to as anti-control of chaos.Anti-control of chaos using is direct time-delay feedback studied in this thesis. Chen circuit is used as a paradigm for analysis and experiment. Firstly, chaos is generated in Chen circuit using the proposed method, phase plot (chaotic attractor), largest Lyapunov exponent, time sequence and power spectrum of state variable are given to confirm the chaos is indeed generated. Circuit experiment is conducted to confirm that the chaos can be generated in Chen circuit. Local bifurcation analysis for the controlled system is conducted using Hopf bifurcation theory. Bifurcation boundary is derived, which is useful for parameters selection of chaos control. the undermined coefficient method is used to calculate heteroclinic orbit in the delay-feedback controlled Chen system. Shil'nikov theorem is used to prove horse-shoe type chaos are indeed generated in the controlled Chen system. The chaotifying control via direct time-delay feedback is simple in structure and easy to realize. The method can realize both the control and anti-control of chaos, which is quite flexible in utilization.We also analysis the Hopf bifurcation of time-delayed immune response model. |
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