Analysis on a diffusive multiple Allee effects predator–prey model induced by fear factors

Abstract This paper is concerned with a diffusive predator–prey system with multiple Allee effects induced by fear factors subject to Neumann boundary conditions. Firstly, we introduce a priori estimates of non-negative and non-trivial solutions. Moreover, nonexistence of non-constant positive solutions are shown for certain parameters ranges. Secondly, we study the stability of non-negative constant solutions by the linearized theory. Then, by choosing the Allee threshold θ as the bifurcation parameter, we investigate the spatially homogeneous and non-homogeneous periodic solutions as well as non-constant steady-state solutions. Finally, some theoretical results are illustrated by numerical simulations.