Dynamics of a predator-prey system incorporating a saturated prey refuge and a fear-induced Allee effect

Abstract

This study focuses on a predator-prey system featuring saturated prey refuges and an Allee effect arising from the prey's fear response. Analytical investigation reveals various aspects, including positivity, the bounds of solutions, and local stability of the coexistence equilibrium point. The local bifurcations (Hopf and transcritical) are discussed. The nature of the limit cycle resulting from a Hopf bifurcation is stated. It is shown that the increasing amount of fear and the Allee effect can produce complicated dynamics that can be controlled by refuge use. Moreover, fear and the Allee effect do not influence the prey density, though they can decrease the predator density at the equilibrium level. Refuge can increase the prey density, but no thet predators. The numerical simulations validate the theoretical outcomes, providing practical insights into the model's behaviour. The novelty of the work is how fear and the Allee effect reduce predator numbers without altering prey numbers at equilibrium density. It also assures that prey refuges raise prey numbers but not the predators.