Bifurcation analysis of a diffusive predator-prey model with schooling behaviour and cannibalism in prey
by Salih Djilali; Abdelheq Mezouaghi; Omar Belhamiti
International Journal of Mathematical Modelling and Numerical Optimisation (IJMMNO), Vol. 11, No. 3, 2021

Abstract: In this paper, we study a predator-prey diffusion model, where we consider two very important factors, herd behaviour and cannibalism in prey. These strange behaviours may exist is some aquatic carnivorous living being such as tuna. Our main objective in this work is to highlight the effect of prey cannibalism on the interaction between predator and prey. In a first step, we make an analysis of the system in the absence of diffusion, where the stability of the equilibrium states and the Hopf bifurcation are treated. Then, the effect of the presence of spatial diffusion is investigated by studying the global stability of the free equilibrium of cannibalism, the Hopf bifurcation and the stability of the periodic solution. The results of the proposed model are then raised, analysed and discussed.

Online publication date: Thu, 29-Jul-2021

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