Mathematical Modeling on a Typical Three Species Ecology

In this chapter, we discuss the stability analysis of mathematical modeling on a typical three species ecology.
The system comprises of a commensal (S1), two hosts S2 and S3 ie., S2 and S3 both benefit S1, without getting
themselves effected either positively or adversely. Further S2 is a commensal of S3 and S3 is a host of both S1,
S2. Here all three species are having limited resources quantized by the respective carrying capacities. The
mathematical model equations constitute a set of three first order non-linear simultaneous coupled differential
equations in the strengths N1, N2, N3 of S1, S2, S3 respectively. In all, eight equilibrium points of the model are
identified. 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
points are illustrated.