Study the Dynamics of Commensalism Interaction with Michaels-Menten Type Prey Harvesting

Abstract

This paper suggests and analyses a model consisting of two commensal populations with Michaelis-Menten type of harvesting for the first population. The first harvested commensal species draws strength from the second hosted species. The overall dynamics are provided to achieve the coexistence, stability and persistence of the equilibrium points for the proposed system. The local bifurcation near the positive equilibrium point is attained. Moreover, numerical simulation using MATLAB is investigated to the impact of the commensalism interaction on the behavior of the planned model. The analysis shows that the role of commensalism prevents the first population from extinction, which could be helpful for the survival of both species.