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.
"Bifurcation Analysis and Sliding Mode Control of Chaotic Vibrations in an Autonomous System." J. Appl. Math. 2014 1 - 14, 2014. https://doi.org/10.1155/2014/726491