The Stability Analysis of a Three Species Syn-Eco-System with Mortality Rates

In this paper, the system comprises of a commensal (S1) common to two hosts S2 and S3 with mortality rate for all the three species. 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 numerical solutions for the growth rate equations are computed using RungeKutta fourth order scheme.