Abstract: Allee effect is very common in population ecology. It is very important to study Allee effect for the survival and development of population. Therefore, we consider the bifurcation solutions of a diffusive predator-prey model with double Allee effect in prey. Firstly, we analyze the stability of constant solutions by stability theory. Secondly, by taking the diffusion coefficient of prey as the bifurcation parameter, we investigate that the local bifurcation solutions evolve from a positive constant solution under strong Allee effect and weak Allee effect, respectively, by local bifurcation theory, which gives a sufficient condition for the existence of coexistence solutions. Finally, we visually present theoretical results by numerical simulation. The results show that the predator and prey can coexist under strong Allee effect or weak Allee effect when the death rate, diffusion rate and predation rate of the predator satisfy certain conditions.

Key words: double Allee effect, predator-prey model, bifurcation solution, stability