Dynamical analysis of a predator-prey model in toxic environment with strong reproductive Allee effect

Abstract

In theoretical ecology, the interaction between predator and prey is a natural phenomenon that greatly influences how communities are organized and how ecological diversity is preserved. In ecology, the effect of toxicity on predator and prey population is a quite important topic nowadays. In this current work, we have taken a look at a Gause-type predator-prey model with a simplified
Holling type IV functional response and a strong Allee effect on the prey population. The effects of toxicity on both predator and prey species have also been introduced. The feasibility and stability requirements of all equilibrium points are properly examined in terms of model parameters. The parametric restrictions of at least one interior equilibrium point have been derived, and the outcomes are illustrated numerically. It is demonstrated that the system undergoes local bifurcations such as transcritical bifurcation, saddle-node bifurcation, Hopf bifurcation, Bogdanov-Takens bifurcation and cusp bifurcation. The basin of attraction of the proposed system is also demonstrated in this study. Numerous numerical examples are used to support each of these theoretical conclusions.