  In the current manuscript, a first two-patch model with Allee effect and
nonlinear dispersal is presented. We study both the ODE case and the PDE case
here. In the ODE model, the stability of the equilibrium points and the
existence of saddle-node bifurcation are discussed. The phase diagram and
bifurcation curve of our model are also given by numerical simulation. Besides,
the corresponding linear dispersal case is also presented. We show that when
the Allee effect is large, high intensity of linear dispersal is not favorable
to the persistence of the species. We further show when the Allee effect is
large, nonlinear diffusion is more favorable to the survival of the population
than linear diffusion. Moreover, the results of the PDE model extends our
findings from discrete patches to continuous patches.
