A Study on Syn-Eco-System Consisting of Two Hosts and One Commensal with Mortality Rate for the First Species

The present investigation is an analytical study of a syn-eco system with mortality rate for the first species. The system comprises of two hosts S1, S2 and one commensal S3 ie, S1 and S2 both benefit S3, without getting themselves affected either positively or adversely. Further S1 and S2 are neutral. The model equations constitute a set of three first order non-linear coupled differential equations. Criteria for the asymptotic stability of all the eight 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.