The impacts of mortality rate and strong Allee effect in a three-species food chain model with Crowley–Martin functional responseodel with Crowley-Martin functional response

Abstract

In ecology, a strong Allee effect is closely associated with population sustainability to extinction. To address this topic, we propose and investigate the intricate features of a three-species food chain model subjected to Crowley–Martin functional response and a strong Allee effect in prey. Here, our focus is to examine how the mortality rate of the middle predator can influence the species interactions. Numerical simulations and stability analysis are utilised to demonstrate the dynamics of the proposed model. The stability analysis is performed using linearization methods on each equilibrium point. Using Sotomayor’s theorem, the occurrence of transcritical bifurcations are investigated. Through bifurcation analysis, we observe bi-stability as well as Hopf and transcritical bifurcations. We observe that all species maintain their viability at medium mortality rates, whereas extinction occurs at low mortality rates.

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