Traveling waves for the nonlocal diffusive single species model with Allee effect

In this paper, we study a nonlocal diffusive single species model with Allee effect. We prove that the model admits positive traveling wave solutions connecting the equilibrium 0 to some unknown positive steady state if and only if the wave speed c≥2r, where r>0r>0 is the intrinsic rate of increase of the species. For the sufficient large wave speed c, we show that the unknown steady state is the unique positive equilibrium. For two types of convolution kernel functions, we investigate the change of the wave profile as the non-locality increases, and illustrate that the unknown steady state may be a positive periodic solution.