Dynamic Analysis of the Symbiotic Model of Commensalism and Parasitism with Harvesting in Commensal Populations

Authors

  • Nurmaini Puspitasari University of Brawijaya
  • Wuryansari Muharini Kusumawinahyu University of Brawijaya
  • Trisilowati Trisilowati University of Brawijaya

DOI:

https://doi.org/10.31764/jtam.v5i1.3893

Keywords:

Commensalism, Parasitism, Michaelis-Menten, Local stabilty analysis.

Abstract

This article discussed about a dynamic analysis of the symbiotic model of commensalism and parasitism with harvesting in the commensal population. This model is obtained from a modification of the symbiosis commensalism model. This modification is by adding a new population, namely the parasite population. Furthermore, it will be investigated that the three populations can coexist. The analysis carried out includes the determination of all equilibrium points along with their existence and local stability along with their stability requirements. From this model, it is obtained eight equilibrium points, namely three population extinction points, two population extinction points, one population extinction point and three extinction points can coexist. Of the eight points, only two points are asymptotically stable if they meet certain conditions. Next, a numerical simulation will be performed to illustrate the model’s behavior. In this article, a numerical simulation was carried out using the RK-4 method. The simulation results obtained support the results of the dynamic analysis that has been done previously.

Author Biographies

Nurmaini Puspitasari, University of Brawijaya

Mathematics Postgraduate Student, University of Brawijaya

Wuryansari Muharini Kusumawinahyu, University of Brawijaya

Brawijaya University Mathematics Postgraduate Lecturer

Trisilowati Trisilowati, University of Brawijaya

Brawijaya University Mathematics Postgraduate Lecturer

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Published

2021-04-17

Issue

Vol. 5 No. 1 (2021): April

Section

Articles

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