Abstract
The purpose of this paper is to examine the stability analysis of a three species ecology with mortality rate for the host. The system comprises of a commensal (S1), two hosts S2 and S3 ie, S2 and S3 both benefit S1, without getting themselves affected either positively or adversely. Further the first species has unlimited resources. The model equations constitute a set of three first order non-linear coupled ordinary differential equations. Criteria for the asymptotic stability of all the four equilibrium states are established. Trajectories of the perturbations over the equilibrium states are illustrated and the global stability of the system is established with the aid of suitably constructed Liapunov’s function and finally fourth order Runge-Kutta method is applied to obtain numerical solutions of the growth rate equations.