Stability on three Typical Syn-Ecology with Limited Resources for the Third Species

Authors

Bitla Hari Prasad, Professor, Gunda Narmada, Polu Sunitha
Department of Mathematics, Chaitanya (Deemed to be University), Telangana State, India.

Abstract

In this paper, the system comprises of a commensal (S1) common to two hosts S2 and S3 with mortality rate for first and second species. Here only the third species has limited resources. The model equations constitute a set of three first order non-linear simultaneous differential equations. Criteria for the asymptotic stability of two 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. Further, the trajectories of the perturbations over the equilibrium states are illustrated.