Email this article DYNAMICAL ANALYSIS OF A PREDATOR - PREY MODEL USING HUNTING STRATEGIES
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Received: 11/08/22 Revised: 22/08/22 Published: 24/08/22Authors
1. Ha Thi Ngoc Yen
, School of Applied Mathematics and Informatics, Hanoi University of Science and Technology2. Nguyen Phuong Thuy, School of Applied Mathematics and Informatics, Hanoi University of Science and Technology
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.
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DOI: https://doi.org/10.34238/tnu-jst.6357
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