Dynamic interactions in a two-species model of the mammalian predator–prey system: The influence of Allee effects, prey refuge, water resources, and moonlights

Abstract

In this paper, a two-species model of mammalian prey and mammalian predator has been developed. It is assumed that mammalian prey species grow logistically in the absence of the Allee effect and mammalian predator species. It is considered that the growth rate of mammalian prey species is affected by Allee. It is assumed that the consumption of mammalian prey is dependent on prey refuge, water resources, and moonlight. Different dynamical behaviours of the model, such as positivity, uniform boundedness, dissipativeness, uniform persistence, bifurcation analysis, etc., have been studied. The local stability of the model has been studied around the equilibrium points. Global stability of the model around the coexistence equilibrium point has been investigated. Transcritical bifurcation of the model with respect to the death rate of mammalian predators has been studied. Also, the existence conditions of Hopf bifurcation with respect to the conversion rate of mammalian prey has been investigated. It is observed that the increased visibility during moonlit nights can significantly impact the hunting success of mammalian predators and the survival strategies of mammalian prey. It is seen that water resources play a crucial role in shaping the dynamics between mammalian prey and predator species. It is found that a moderate increase in the Allee effect can stabilize populations by enhancing cooperation and survival at low densities, a higher rate of increase can lead to severe instability and potential population crashes Finally, some numerical simulation results have been presented to validate the analytical findings.