Mathematical analysis of harvested predator-prey system with prey refuge and intraspecific competition

Authors

  • Alanus Mapunda Department of Mathematics and Statistics, Mbeya University of Science and Technology, P. O. Box 131, Mbeya Tanzania
  • Thadei Sagamiko Department of Physics, Mathematics and Informatics, Dar es Salaam University College of Education, University of Dar es Salaam, P. O. Box 2329, Dar es Salaam Tanzania

DOI:

https://doi.org/10.4314/tjs.v47i2.28

Keywords:

Prey refuge, bifurcation, harvesting, intraspecific competition, phase portrait

Abstract

In this paper, a predator-prey relationship in the presence of prey refuge was studied. The analysis of the dependence of locally stable equilibrium points on the parameters of the problem was carried out. Bifurcation and limit cycles for the model were analyzed to show the dynamical behaviour of the system. The results showed that the system is stable at a constant prey refuge m = 0.3 and prey harvesting rate H = 0.3. However, increasing m and decreasing H or vice versa, the predator-prey system remains stable. It was further observed that for a constant prey refuge m ≥ 0.78, the predator population undergoes extinction. Therefore, m was found to be a bifurcation parameter and m = 0.78 is a bifurcation value.

Keywords: Prey refuge, bifurcation, harvesting, intraspecific competition, phase portrait

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Published

2021-05-27

Issue

Vol. 47 No. 2 (2021)

Section

Articles

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