Influence of predator incited fear and interference competition in the dynamics of prey-predator system where the prey species are protected in a reserved area

Abstract

In this article, we contemplated a prey-predator model where the dwelling place of prey species is partitioned into two areas, namely reserved area and unreserved area. Both the prey and predator species are allowed in unreserved area to access their living resources; whereas reserved area is protected only for prey species and predators are not allowed by any means in this area. At the unreserved zone, predation is allowed and prey species are in fear of predation by the predators. As a consequence, it is assumed that prey species in unreserved zone shows many anti-predator behaviour and defense mechanism (due to fear of predation), which create the shortage of food and compels the predators to engage into a clash among themselves. After completion of model construction, the persistence of all the species and well-posedness of the model system have been studied. The existence and stability criterion of all the equilibrium points have been found. Furthermore, bifurcation analysis is done and direction of Hopf-bifurcation is detected using center manifold theory. Through model analysis and rigorous numerical simulation, it is observed that cost of fear and interference competition among the predators cooperatively determine the eco-dynamics of the model system in a complex manner. Finally, we have plotted various 2-parameter bifurcation diagrams near the hopf-point to explore the role of different parameters involved in the model system.