Stability Analysis of a Three Species Non-linear Eco-system with Restricted Resources

Abstract

The aim of this paper is to introduce the model and the study of a three species non linear ecosystem with restricted resources. In this paper, the system comprises of two species hosts S 1 , S 2 and one commensal species S 3 . Further, S 1 and S 2 are neutral and all the three species posses restricted resources. Commensalism is a symbiotic interaction between two or more populations which live together, and in which only one of the populations (commensalism) is beneted while the other (host) is not effected. The model equations constitute a set of three first order non-linear simultaneous differential equations. Criteria for the asymptotic stability of all the eight equilibrium states are established. The system would be stable if all the characteristic roots are negative, in case they are real, and have negative real parts, in case they are complex. 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.