Bistability and tristability in a predator-prey model with strong allee effect in prey

Understanding the Allee effect on endangered species is crucial for ecological conservation and management as it highly affects the extinction of a population. Due to several ecological mechanisms accounting for the Allee effect, it is necessary to study the dynamics of a predator-prey model incorporating this phenomenon. In 1999, Cosner et al. [Effects of spatial grouping on the functional response of predators, Theor Popul Biol 56:65-75, 1999] derived a new kind of functional response by considering spatially grouped predators. This paper deals with the dynamical behavior of a predator-prey system with functional response proposed by Cosner et al., and the growth of the prey population suffers a strong Allee effect. We find that the system undergoes various types of bifurcations such as Hopf bifurcation, saddle-node bifurcation, and Bogdanov-Takens bifurcation. We also observe that the model exhibits bistability and two different types of tristability phenomena. Our findings reveal that for such a kind of multistability in ecological systems, the initial population size plays a crucial role and also impacts the system's state in the long term.