Dynamic analysis of discrete predator–prey model with anti-predator behavior

The dynamical behavior of a discrete predator–prey model with anti-predator behavior is analyzed in this paper. The existence, stability, and local dynamics of the fixed points are discussed. By using Center Manifold Theorem and bifurcation theory, we study the existence of periodic-doubling bifurcation. The Neimark–Sacker bifurcation and stability of the bifurcated invariant curve are discussed as well. Moreover, the numerical simulations are presented to illustrate the results obtained in this paper. It is worth mentioning that the impact of anti-predator behavior on the system is revealed through numerical simulations.