Bifurcation Analysis of a Predator–Prey Model With Degenerate Diffusion and Multiple Allee Effects in Predators

Cooperative behaviors among individuals are prevalent in ecosystems and can trigger the Allee effect. To understand the combined effects of the cooperation‐mediated Allee effect and mate limitation on population dynamics, a degenerate reaction–diffusion model is formulated by incorporating the component Allee effect and hunting cooperation. For the non‐spatial scenario, the analytical results and numerical simulations show that the system exhibits rich dynamics such as cyclic phenomena, bistability, and Bogdanov–Takens bifurcation. For the reaction–diffusion model, sufficient conditions are derived for Turing instability and the existence of Hopf bifurcation, Turing bifurcation, and Turing–Hopf bifurcation are characterized. The key findings reveal that low‐intensity component Allee effect and moderate cooperation can enhance the existence of predators and prey, while high‐intensity component Allee effect and excessive cooperation may lead to the extinction of some population and spatiotemporal chaos. Meanwhile, degenerate diffusion can change the spatial structure of periodic solutions. Furthermore, the system exhibits complex critical transitions and spatiotemporal patterns near the Turing–Hopf bifurcation point, which provide valuable insights on species conservation and evasion of tipping points in complex ecosystems.