Bifurcation Control for a Duffing Oscillator with Delayed Velocity Feedback

In this paper, a Duffing oscillator model with delayed velocity feedback is considered.Applying the time delayed feedback control method and delayed differential equation theory, we establish some criteria which ensure the stability and the existence of Hopf bifurcation of the model.By choosing the delay as bifurcation parameter and analyzing the associated characteristic equation, the existence of bifurcation parameter point is determined.We found that if the time delay is chosen as a bifurcation parameter, Hopf bifurcation occurs when the time delay is changed through a series of critical values.Some numerical simulations show that the designed feedback controllers not only delay the onset of Hopf bifurcation, but also enlarge the stability region for the model.