Hydra effect and dynamics of predation with double Allee effect in prey and intraspecific competition in predator

In this paper, we investigate a prey-predator system with intraspecific competition in predators and double Allee effect in prey. We focus on dynamical behaviors of induced by strong Allee effect and predator intraspecific competition. First, we analyze the existence and stability of equilibria. To systematically explore the double Allee effect’s impact, we partition the parameter space into two regions to determine the number of interior equilibria in each case and present corresponding bifurcation diagrams and phase portraits. Comparing with systems lacking either the double Allee effect in the prey or predator intraspecific competition show that the double Allee effect in prey, combined with excessive predation, may cause extinction of both species. Moreover, predator intraspecific competition among predator induces the hydra effect, thereby mitigating over-exploitation and promoting predator-prey coexistence.