Dynamics of a spatially coupled model with delayed prey dispersal

Abstract

Dispersal of species from one region to another one is a common occurrence in ecology. Several studies have been conducted on predator–prey interactions subjected to population dispersal between patches. In this paper, we consider a two-patch Rosenzweig-MacArthur predator-prey model with prey dispersal. In absence of predator, the movement of prey is density-independent. Predator-influenced prey dispersal is also taken into account because predators have a potential to control prey movement. Travelling time (time delay) linked with the movement mechanism among the prey community is incorporated. The positivity and boundedness of the solutions in the spatially coupled system are established. Stability behaviours of the coexisting equilibrium are explored by considering delay as the bifurcating parameter. It is found that, delayed prey dispersal can potentially alter the stability (resp. instability), and even causes stability switching (resp. instability switching) around the interior equilibrium. However, after some consecutive changes in stability, the equilibrium undergoes instability for larger delay. Analysis of the stability is performed by estimating the distance between critical values of the time delay. In addition, numerical examples are provided to illustrate the findings. © 2021 Informa UK Limited, trading as Taylor & Francis Group.