• ON THE STABILITY OF A TYPICAL THREE SPECIES SYN-ECO-SYSTEM

Abstract

The present paper deals with an investigation on a typical three species syn eco-system. 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. Trajectories of the perturbations over the equilibrium points are illustrated. Further we establish global stability of a four spices syn-eco system by constructing a suitable Liapunov’s function.