Dynamics of predator–prey populations with allee effects under the influence of two generalist predators - Pratama, Rian Ade; Suryani, Dessy Rizki; Ruslau, Maria F V (Universitas Islam Negeri Raden Intan Lampung, 2025)
In this study, we analyze a predator–prey model incorporating a Holling type II functional response, an Allee effect in the prey population, and generalist predator species. The proposed interaction model is formulated as a nonlinear differential system involving three species: one prey species and two generalist predator species. The research methodology combines literature review and analytical investigation. The objectives are to examine the equilibrium points, assess stability using the Routh–Hurwitz criteria, and perform numerical simulations to illustrate population growth trajectories. The analysis reveals eleven equilibrium points, consisting of trivial, semi-trivial, and coexistence equilibria. Among the coexistence equilibria, only one satisfies the local stability conditions, as determined by the characteristic equation associated with the Routh–Hurwitz criteria. The characteristic equation of the model is a complex quartic polynomial. Ecologically, such local stability conditions ensure the persistence of all species within the ecosystem. Numerical simulations are also provided for the proposed model, demonstrating stable conditions for all three populations. However, the population growth patterns of the three species differ significantly. The prey population exhibits pronounced fluctuations: initially showing a gradual change, followed by a rapid increase once predation occurs, eventually reaching a stable state. Interestingly, during predation events, the overall prey population size experiences substantial growth. When predation proceeds without significant hindrance, predator populations also increase simultaneously. The interplay between the Allee effect and the Holling type II functional response plays a critical role in determining the numerical dynamics of the predator–prey system.