Hybrid control of Hopf bifurcation in a two prey one predator system with time delay

This paper is concerned with Hopf bifurcation analysis for a two prey one predator system with time delay. The state feedback and parameter perturbation are used to delay the onset of Hopf bifurcation or make the bifurcation disappear. The sufficient conditions for the local stability and existence of local Hopf bifurcation of the system are obtained. In particular, special attention is paid to the direction of Hopf bifurcation and the stability of the bifurcated periodic solutions. Finally, some numerical simulations are presented to show that the hybrid controller is efficient in controlling Hopf bifurcation.