Bifurcation and Control for a Predator-Prey System With Two Delays

This brief mainly studies the dynamic analysis and control problem for the Leslie-Gower predator-prey system, which is established by a delay-differential equation. We use the Euler scheme to derive the discrete form of Leslie-Gower model. By discussing the associated characteristic equation, its dynamics properties, including stability analysis and Neimark-Sacker bifurcation, are investigated. Furthermore, we use the center manifold reduction and normal form theory to show the directions of Neimark-Sacker bifurcation, and we also analyze the stability of periodic bifurcation solution. In order to achieve effective control of the above bifurcation, we proposed a novel delayed feedback control scheme. Finally, an simulation example is given to verify the effectiveness of the main conclusion.