Bifurcation control of an incommensurate fractional-order Van der Pol oscillator

In this paper, a dynamic state feedback is applied to control Hopf bifurcations arising from an incommensurate fractional-order Van der Pol oscillator. The control parameter of the incommensurate fractional-order Van der Pol system is chosen as the bifurcation parameter. It is shown that in the absences of the dynamic state feedback controller, the incommensurate fractional-order system loses the stability via the Hopf bifurcation early and can maintain the stability only in a certain domain of the control parameter. When the state feedback controller is applied to the incommensurate fractional-order system, the onset of the undesirable Hopf bifurcation is postponed. Thus, the stability domain is extended and the system possesses the stability in a larger parameter range. Numerical simulations are given to illustrate the validity of the dynamic state feedback controller in bifurcation control of the incommensurate fractional-order Van der Pol system.