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

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

Impact of Cooperation and Intra-Specific Competition of Prey on the Stability of Prey–Predator Models with Refuge

“…The stabilizing role of refuge in prey-predator systems was shown many years ago, and since then, various aspects of prey-predator systems with refuge have been analyzed using Holling type II nonlinearities [30,31]. Mapunda et al [32] and Kumar et al [30] showed the effect of intra-specific competition among predators on the prey-predator system in their respective studies. The effect of cooperation among predators on the preypredator system through cooperative hunting strategies was shown by Saha and Samanta in their study [33].…”