Abstract:

We studied the Hopf bifurcation  and Hopf bifurcation control for a Van der PolDuffing system. First of all, we analyzed the Hopf bifurcation and designed the linear and nonlinear state feedback controller for the autonomous system. Then, we designed a state feedback controller based on Washout filter, and discussed the impact of the control gain on the existence of the Hopf bifurcation and the limit cycle amplitude. Results show that selecting appropriate control gain can not only control the occurrence of Hopf bifurcation, but also change the size of the limit cycle amplitude.

Key words: Hopf bifurcation, Washoutfilter; , limit cycle amplitude, bifurcation control