Non-smooth dynamics emerging from predator-driven discontinuous prey dispersal

Abstract

In ecology, the refuge protection of the prey plays a significant role in the dynamics of the interactions between prey and predator. In this paper, we investigate the dynamics of a non-smooth prey-predator mathematical model characterized by density-dependent intermittent refuge protection of the prey. The model assumes the population density of the predator as an index for the prey to decide on when to avail or discontinue refuge protection, representing the level of apprehension of the prey by the predators. We apply Filippov's regularization approach to study the model and obtain the sliding segment of the system. We obtain the criterion for the existence of the regular or virtual equilibria, boundary equilibrium, tangent points, and pseudo-equilibria of the Filippov system. The conditions for the visibility (or invisibility) of the tangent points are derived. We investigate the regular or virtual equilibrium bifurcation, boundarynode bifurcation and pseudo-saddle-node bifurcation. Further, we examine the effects of dispersal delay on the Filippov system associated with prey vigilance in identifying the predator population density. We observe that the hysteresis in the Filippov system produces stable limit cycles around the predator population density threshold in some bounded region in the phase plane. Moreover, we find that the level of apprehension and vigilance of the prey play a significant role in their refuge-dispersion dynamics.

The Effects of Varying Predator Dispersal Strength on Prey-Predator Dynamics with Refuge Process

“…They proposed conditions ensuring the uniform asymptotic stability of the positive equilibrium point. In the investigation by Bhattacharyya and Chattopadhyay [19], the focus was on the non-smooth dynamics resulting from predator-driven prey dispersal and the behaviour of prey refuge. The research highlighted that highly apprehensive prey preferred longer refuge stays, while hypervigilant prey frequently changed habitats.…”