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Influence of Allee effect on the spatiotemporal behavior of a diffusive predator-prey model with Crowley-Martin type
Lakshmi Narayan Guin1, Pallav Jyoti Pal2, Jawaher Alzahrani3
1Department of Mathematics, Visva-Bharati, Santiniketan, West Bengal, 731235, India.
Abstract:
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.
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