Stability analysis of two mutually interacting species with unlimited resources for both the species

Abstract

The present paper deals with an analytical investigation of a model of two species mutually interacting with resources for both the species being unlimited. The model is characterized by a coupled system of first order non-linear ordinary differential equations. Only one equilibrium point is identified and its stability criteria are derived. It is observed, in case when the death rate of the second species is greater than its birth rate, there exist only one equilibrium point. Stability of the equilibrium point and the solutions for the linearized perturbed equations are obtained. However when the death rate is greater than the birth rate for both the species, there exists two equilibrium points. We derived their stability criteria and obtained the solutions of the linearized perturbed equations.