Lyapunov function for two-species mutualism model with constant harvesting. Mathematical Sciences and Informatics Journal (MIJ), 1 (2). pp. 1-11. ISSN 2735-0703 (2020)
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.
| Item Type: | Article |
|---|---|
| Keywords: | Mutualism Model, Constant Harvesting, Global Stability, Lyapunov Function, Equilibrium |
| Taxonomy: | By Subject > Computer & Mathematical Sciences > Mathematics By Subject > Computer & Mathematical Sciences > Statistics |
| Local Content Hub: | Subjects > Computer and Mathematical Sciences |
| Depositing User: | Nur Aida Rousli |
| Date Deposited: | 12 Oct 2021 23:38 |
| Last Modified: | 17 Oct 2021 06:45 |
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