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A Mathematical Model of Four Species Syn-Ecosymbiosis Comprising of Prey-Predation, Mutualism and Commensalisms-III(Two of the Four Species are washed out States)

R. Srilatha, B. Ravindra Reddy and N. Ch. Pattabhiramacharyulu.

This investigation deals with a mathematical model of a four species (S1, S2, S3 and S4) Syn- Ecological system (Two of the four species are washed out states). S2 is a predator surviving on the prey S1: the prey is a commensal to the host S3 which itself is in mutualism with the fourth species S4. Further S2 and S4 are neutral. The model equations of the system constitute a set of four first order non-linear ordinary differential coupled equations. In all, there are sixteen equilibrium points. Criteria for the asymptotic stability of six of the sixteen equilibrium points: Two of the four species are washed out states only are established in this paper. The linearized equations for the perturbations over the equilibrium points are analyzed to establish the criteria for stability and the trajectories illustrated