Prey-Predator Model for Awash National Park, Oromia, Ethiopia and Its Stability Analysis with Simulations

Abstract

In this paper, we discuss a model of two-space food chain consisting of the population of ecology of foxes (the predator) and rabbits (prey) in Awash National park, Ethiopia. The study is based on formulation of a mathematical model to study the dynamics of the population densities and analyzing the stability of equilibrium points of the prey-predator model. The aim of this model is to explore the behavior of a simple model by considering a population of foxes, and rabbits. This model is constituted by a system of nonlinear decoupled ordinary differential equations. By using perturbed method, we identify the nature of the system at each equilibrium point. The stability analysis of a prey-predator model is discussed with numerical simulations.