DYNAMICAL ANALYSIS OF A PREDATOR - PREY MODEL USING HUNTING STRATEGIES

Abstract

In this paper, we establish a new prey-predator model using game theory with solitary hunting or pack hunting strategies. The model includes a fast-time scale and a slow-time scale to investigate the effect of predator behavior on the ecosystem. In our model, we assume that the switch between hunting strategies and hawk-dove tactics happens on a fast-time scale, while the development of the species of prey intrinsic growth, predator mortality, and hunting process, takes place on a slow-time scale. We use the differential equations theory and the aggregated method to study the model’s well-posedness and the properties of its solution, such as positivity, boundedness, and stability. It is shown that the coexistence of prey and predator might be in a steady state or a chaotic state. Some numerical simulations illustrate the theoretical results in cases of stable equilibrium and chaotic equilibrium are given. Discussions about predators' behavior and the ecosystem's development are also provided.