Influence of Allee effect on the spatiotemporal behavior of a diffusive predator–prey model with Crowley–Martin type response function

The present paper is dealt with a predator–prey model in which the growth of the prey population is influenced by the Allee effect while the predator species are contended with the prey population following the Crowley–Martin type response function. The proposed model is comprehensively analyzed in terms of stability and manifestation of bifurcation of the system. The system unveils the bi-stability together with the existence of a separatrix. In view of the eminence of spatial ecology, the dynamical complexity emanating from the induction of the Allee effect in prey species of a Crowley–Martin reaction–diffusion predator–prey model is also investigated profoundly. The results of numerical simulations reveal that the present system dynamics is motivated by both the Allee effect and diffusion-controlled pattern formation growth to hot spots, stripe-hot spot mixtures, stripes, labyrinthine, stripe-cold spot mixtures, and cold spots replication. The theoretical consequences of the spatiotemporal model under study are validated through numerical simulations.