Global bifurcation in a diffusive Beddington-DeAngelis predator–prey model with population flux by attractive transition

Abstract

The study involves examining the global bifurcation structure associated with the nonconstant steady states of a reaction-diffusion predator-prey system where both the species interact in accordance with the Beddington DeAngelis response and the flux of the predator incorporates attractive transition. We consider the magnitude of population flux by attractive transition as the bifurcation parameter and employ the Crandall-Rabinowitz bifurcation theorem to study the global bifurcation structure associated with the problem. We have also derived some a priori estimates associated with the problem and carried out numerical simulations to support our theoretical results. This work can be regarded as the first step towards inclusion of population flux by attractive transition in scenarios where interactions are governed by complex functional responses.