Mapunda, AlanusSagamiko, Thadei2025-02-282025-02-2820210856-17612507-7961https://dx.doi.org/10.4314/tjs.v47i2.28https://repository.must.ac.tz/handle/123456789/234This research article was published by Tanzania Journal of Science in 2021In 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 valueen-USArticle