Stability and Neimark-Sacker bifurcation behavior of predator-prey model with refuge.

*(Chinese. English summary)*Zbl 07267309Summary: A kind of predator-prey model with refuge was approached. Stability and Neimark-Sacker bifurcation behavior of the model were discussed in detail. The difference equation corresponding to this kind of model was obtained at first by function transformation. And the sufficient condition of the positive equilibrium’s local asymptotic stability was derived by the linear stability theory. Secondly, with parameter variation, normal form theory and center manifold projection method were used to deduce the cases of the system that caused flip bifurcation and Neimark-Sacker bifurcation into chaos. In the last part, numerical simulations were experimented to verify the correction of the results approached in this paper.