[01] B. Hari Prasad, Department of Mathematics, Chaitanya Degree College (Autonomous), Hanamkonda, Telangana State, India.

The present investigation is a study on syn ecology with mortality rate for the first and second species. The system comprises of two hosts S1, S2 and one commensal S3 i.e. 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 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 and the numerical examples for the growth rate equations are computed using Runge-Kutta fourth order method.

Commensal, Host, Liapunov’s Function, Stable, Trajectories, Unstable

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