Two Species Interact in the Ecosystem with Michaelis Menten Harvesting Rate and Holling Type II Functional Response

Abstract

In the study, a mathematical model was proposed two nonlinear ordinary differential equation to depict the relationship between prey and predator population.  This approach provides insights into the behaviors of prey-predator interaction.  In the context of our model, the Holling type II functional response is accompanied, by a Michaelis Menten harvesting rate on prey.  In the investigation of the presence, boundedness of positive outcomes, and local stability at each feasible equilibrium point of this model are explored.  The model includes four equilibrium points, with two being unstable, whereas the others are contingent upon specific conditions.  Utilizing the Bendixson-Dulac criterion, the global stability of the equilibrium point representing predator extinction is analyzed.  A theorem presents the global stability criteria.  Lastly, two instances of numerical analysis demonstrate the validity of the theoretical approach