Stability Analysis Of Three Species Ecological Commensalism
Abstract
The present paper deals with an investigation on three species ecological commensalism. Here, all the 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. All possible 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. Criteria for the asymptotic stability of all eight equilibrium points is established and also the global stability is discussed by using suitable Liapunov’s function. Further the numerical solutions for the growth rate equations are computed using Runga Kutta fourth order method.
