Title: Bifurcation analysis of a diffusive predator-prey model with schooling behaviour and cannibalism in prey

Authors: Salih Djilali; Abdelheq Mezouaghi; Omar Belhamiti

Addresses: Laboratoire d'Analyse Non Linéaire et Mathématiques Appliquées, Abou Bekr Belkaid University of Tlemcen, Algeria; Department of Mathematics and Computer Science, Hassiba Benbouali University of Chlef, Algeria ' Laboratoire de Mathématiques Pures et Appliquées, Abdelhamid Ibn Badis University of Mostaganem, Algeria; Department of Mathematics and Computer Science, Hassiba Benbouali University of Chlef, Algeria ' Laboratoire de Mathématiques Pures et Appliquées, Department of Mathematics and Computer Science, Abdelhamid Ibn Badis University of Mostaganem, Algeria

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.

Keywords: predator-prey model; cannibalism; herd behaviour; spatial diffusion; Hopf bifurcation.

DOI: 10.1504/IJMMNO.2021.116676

International Journal of Mathematical Modelling and Numerical Optimisation, 2021 Vol.11 No.3, pp.209 - 231

Received: 29 Nov 2019
Accepted: 16 Jul 2020
Published online: 29 Jul 2021 *

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