• A MATHEMATICAL SYN-ECOLOGICAL MODEL COMPRISING OF PREY-PREDATOR, HOST-COMMENSAL, MUTUALISM AND NEUTRAL PAIRS

Abstract

This investigation deals with a mathematical model of a four species (S1, S2, S3 and S4) Syn-Ecological system. S2 is a predator surviving on the prey S1. The predator S2 is a commensal to the host S3. The pairs S2 and S4, S1 and S3 are neutral. The mathematical model equations characterizing the syn-ecosystem constitute a set of four first order non-linear coupled differential equations. There are in all sixteen equilibrium points. Criteria for the asymptotic stability of the sixteen equilibrium points are established. The linearised equations for the perturbations over the equilibrium point are analyzed to establish the criteria for stability. Trajectories of the perturbations have been illustrated. Also global stability is discussed by Lyapunov’s function. Further analytical stability criteria are supported by numerical simulations using Mat lab.