Neimark–Sacker Bifurcation of a Discrete-Time Predator–Prey Model with Prey Refuge Effect

In this paper, we deduce a predator–prey model with discrete time in the interior of R+2 using new method to study its local dynamics and Neimark–Sacker bifurcation. Compared continuous models, ones have many unique properties that help understand changing patterns biological populations from completely perspective. The existence stability three equilibria are analyzed, formation conditions bifurcation around positive equilibrium point established center manifold theorem theory. An attracting closed invariant curve appears, which corresponds periodic oscillations between predators prey over long period time. Finally, some numerical simulations their meanings given reveal complex dynamical behavior.