Complex Dynamical Behaviors of a Discrete Modified Leslie-Gower Predator-Prey Model with Prey Harvesting

Recently, the research on the modified Leslie–Gower model has become an appealing topic. Due to economic efficiency and the complexity of discrete models, we investigate a discrete modified Leslie–Gower predator–prey model with prey harvesting in this paper. The stability of fixed points and bifurcations of the interior fixed points are studied. According to bifurcation theory and normal forms, we derived the conditions of codimension 2 bifurcations occurred, including 1:1 strong resonance bifurcation and fold-flip bifurcation. These two bifurcations are unusual in bifurcation analysis on discrete systems. In addition, the continuation curves, bifurcation diagrams, and phase diagrams are used to demonstrate theoretical results. Our study shows the interesting dynamics of this model that are very different from the continuous one.