Stability and Neimark-Sacker Bifurcation of Leslie-Gower Predator-Prey System with Two Delays

Neimark-Sacker bifurcation of a delay differential equation modeling two-enterprise interaction mechanism is investigated. For the demands of computer simulation applications, the discrete-time two-enterprise interaction model is proposed by using the forward Euler scheme. By discussing the characteristic equation of linearized part, the local stability criterion of the positive fixed point is presented. Time lag is selected as the bifurcation parameter. Then it is demonstrated that variation of time lag may result in Neimark-Sacker bifurcation. Furthermore, derivations for the directions and stability of Neimark-Sacker bifurcation are also given. Finally, we simulate the main results.