Allee effect in a diffusive predator–prey system with nonlocal prey competition

Nonlocal competition and Allee effect have extensively been considered in modeling population dynamics of species independently. This paper introduces two aspects, which prey has nonlocal competition and predator is subject to Allee effect, in a predator–prey system to investigate the effects of predation on the spatial distribution of prey. The conditions for the coexistence equilibrium point to remain stable and to undergo spatially inhomogeneous Hopf bifurcation and Turing bifurcation have been studied. In the absence of Allee effect, we find that the coexistence equilibrium point of the system is locally asymptotically stable independent of the nonlocal competition. In the presence of Allee effect, nonlocal prey competition can destabilize the coexistence equilibrium point. Numerical simulations are carried out to illustrate the theoretical results. The amplitude of oscillation solution for nonlocal prey competition system is larger than local prey competition system until oscillation solution evolves to periodic solution. Also, nonlocal prey competition term can drive a spatially inhomogeneous Hopf bifurcation, and the spatially inhomogeneous periodic solution emerges. Moreover, it is showed that when the habitat domain is larger, comparing with local prey competition system, the prey diffusion coefficient of system with nonlocal prey competition needs to be larger for two species coexistence in the spatially homogeneous form.