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We study the bifurcations and sliding mode control of chaotic vibrations in an autonomous system. More precisely, a Hopf bifurcation controller is designed so as to control the unstable subcritical Hopf bifurcation to the stable supercritical Hopf bifurcation. Research result shows that the control method can work very well in Hopf bifurcation control. Besides, we controlled the system to any fixed point and any periodic orbit to eliminate the chaotic vibration by means of sliding mode method. And the numerical simulations were presented to confirm the effectiveness of the controller. [ABSTRACT FROM AUTHOR]

In order to further understand a Lorenz-like system, we study the stability of the equilibrium points and the existence of Hopf bifurcation by center manifold theorem and normal form theory. More precisely, we designed a washout controller such that the equilibrium E0 undergoes a controllable Hopf bifurcation, and by adjusting the controller parameters, we delayed Hopf bifurcation phenomenon of the equilibrium E+. Besides, numerical simulation is given to illustrate the theoretical analysis. Finally, two possible electronic circuits are given to realize the uncontrolled and the controlled systems. [ABSTRACT FROM AUTHOR]