Bifurcations of a modified Leslie-Gower predator-prey model with fear, Allee effect and hunting cooperation strategy

Abstract

The fear preoften leads to changes in the physiological characteristics of the prey. Different stages of prey exhibit different physiological behaviours, such as susceptibility to predator risk, which often leads to Allee effect. Taking into account the influence of these factors, a modified Leslie-Gower predator-prey model with Allee effect and stage structure is constructed in this paper. By use of variational technique and normal form theory, the criteria assuring the appearance of transcritical bifurcation, saddle-node bifurcation, Hopf bifurcation and its direction are all established. Specially, such codimension 2 bifurcations as Bautin bifurcation and Bogdanov-Takens bifurcation are presented. The bubble phenomenon and bistability are detected. All theoretical findings are verified by numerical examples. The biological effects of fear level, Allee effect and stage structure on system stability are analysed.

Keywords: 34C23; 92D25; Allee effect; Fear; bifurcation; hunting cooperation; stage structure.