Hybrid control of Hopf bifurcation in a Lotka-Volterra predator-prey model with two delays

Hybrid control of Hopf bifurcation in a Lotka-Volterra predator-prey model with two delays

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Abstract In this paper, the Hopf bifurcation control for a Lotka-Volterra predator-prey model with two delays is studied by using a hybrid control strategy.By analyzing the associated characteristic Eye Serum equation, its local stability and the existence of Hopf bifurcation with respect to both delays are established.In addition, the onset of an inherent Advent calendars bifurcation is delayed.

Based on the normal form theory and the center manifold theorem, explicit formulas are derived to determine the direction of Hopf bifurcation and stability of the bifurcating periodic solution.Numerical simulation results confirm that the hybrid controller is efficient in controlling Hopf bifurcation.