Lyapunov Function for Two-species Mutualism Model with Constant Harvesting

Abstract

In this paper, the researcher proposes a simple mathematical model consisting of mutualistic interactions among two-species with constant harvesting. Mutualism is one kind of interaction that ends up being a win-win situation for both species involved. The interacting species benefit from this interaction and ultimately are better adapted for continuous existence. The harvesting function is implemented to describe the rate of removal of the species. This paper aims to investigate the global stability of the unique positive equilibrium point of the model. The global stability of the model is studied by using Lyapunov function method. By constructing a suitable Lyapunov function, it has been proven that the unique positive equilibrium point is globally asymptotically stable in a nonlinear system. Finally, numerical simulation is shown to illustrate theoretical results and to simulate the trajectories around the stable equilibrium point. From the numerical analysis, it is observed that both the species persist.