Open AccessMathematical analysis of harvested predator-prey system with prey refuge and intraspecific competition
Author(s) -
Alanus Mapunda,
Thadei Sagamiko
Publication year - 2021
Publication title -
tanzania journal of science/tanzania journal of science
Language(s) - English
Resource type - Journals
eISSN - 2507-7961
pISSN - 0856-1761
DOI - 10.4314/tjs.v47i2.28
Subject(s) - intraspecific competition , predation , phase portrait , extinction (optical mineralogy) , predator , mathematics , population , bifurcation , competition (biology) , ecology , biology , physics , demography , paleontology , quantum mechanics , nonlinear system , sociology
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