Bifurcation Analysis of a General Discrete Predator–Prey Model with Fear Effect

This study presents a comprehensive bifurcation analysis of a generalized discrete predator–prey model that incorporates the fear effect, extending previous research by examining the impact of fear on system dynamics through a novel theoretical framework. Initially, we generalize some existing discrete predator–prey models with fear effect, then analyze the dynamical properties such as the existence of the fixed points, the local stability and possible bifurcations for the discrete model. With the aid of bifurcation theory and the central manifold theorem, we provide sufficient conditions for the model to undergo a flip bifurcation and a Neimark–Sacker bifurcation at the positive fixed point by taking the degree of fear as the bifurcation parameter. Furthermore, we establish criteria for the stability of bifurcated periodic orbits and invariant curves. The obtained results substantially extend and improve some existing ones in the literature. Two numerical examples and simulations are given to check the validity of the theoretical results, and to reveal that fear effect has a significant impact on dynamical behaviors of the predator–prey system.