Multistability in a predator–prey model with generalist predator and strong Allee effect in prey

In this study, we analyze a generalist predator–prey model that includes a strong Allee effect in the prey population. We investigate the positivity and boundedness of solutions, identify ecologically relevant equilibrium points, and determine their stability conditions. Further, we analyze the transcritical, saddle-node, Hopf, Bogdanov-Takens, generalized-Hopf, and cusp bifurcations. Our numerical investigation shows that the model exhibits multiple stable states under similar parametric conditions, driven by bifurcation scenarios linked to the Allee effect. It also underscores the significant role of additional foods for predators in shaping system dynamics, unveiling scenarios ranging from the extinction of predators to their persistence, and the coexistence of both the species. Furthermore, our study delves into the impact of environmental white noise on predator–prey dynamics, introducing stochastic elements. We explore noise-induced transitions between two stable states within the system. Overall, our study highlights the complex dynamics of predator–prey interactions, emphasizing the role of Allee effect and additional food sources.