The present investigation is on an analytical and numerical study of a typical three species syn-eco system with mortality rate for commensal. The system comprises of a commensal (S1), two hosts S2 and S3 where 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 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. Further the global stability of the system is established with the aid of suitably constructed Liapunov’s function and the numerical solutions for the growth rate equations are computed using Runge-Kutta fourth order scheme.
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