Mathematical Model of the Dynamics of three Different Species in Predator-Prey System

Abstract

To understand how organisms interact with themselves and their surroundings, it is necessary to use mathematical models to explore the science of multispecies cohabitation. This paper studied the interaction between three species of animals (Lion, Leopard, and Hare) in an environment using a formulated predator-prey model of system of three nonlinear differential equations of first order with five equilibrium points. The equilibrium points were found using the Routh Hurwitz Stability Criterion to be locally asymptotically stable. It was also established that the solution of the model exist and are all positive for any t≥0. Some numerical simulations were carried out to show the analytical solution of the model and the results presented. The results show that the predator-prey presented in this work can be used perfectly to study any species interaction with the same nature with the ones considered in this paper. For further studies, this model can be extended to include four or more species interactions