Fear Induced Multistability in a Predator-Prey Model

Abstract

In ecology, the predator’s impact goes beyond just killing the prey. In the present work, we explore the role of fear in the dynamics of a discrete-time predator-prey model where the predator-prey interaction obeys Holling type-II functional response. Owing to the increasing strength of fear, the system becomes stable from chaotic oscillations via inverse Neimark–Sacker bifurcation. Extensive numerical simulations are carried out to investigate the intricate dynamics for the organization of periodic structures in the bi-parameter space of the system. We observe fear induced multistability between different pairs of coexisting heterogeneous attractors due to the overlapping of multiple periodic domains in the bi-parameter space. The basin sets of the coexisting attractors are obtained and discussed at length. Multistability in the predator-prey system is important because the dynamics of the predator and prey populations in the critical parameter zone becomes uncertain.