InternationaleJournals

A model of two mutually interacting species with unlimited resources for both the species

 B. Ravindra Reddy1, N. Phani Kumar2 and N. Ch. Pattabhi Ramacharyulu3 

1 Vidya Jyothi Institute of Technology, C.B. Post, Hyderabad-500075, India.

2 Faculty in Mathematics, Malla Reddy Engineering College, Secunderabad, India.

3 Professor (Retd.) of Mathematics, NIT, Warangal 506004, India.

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.

 


   International eJournal of Mathematics and Engineering

   Volume 1, Issue 1II, Pages:  372 - 381