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

Stability and bifurcation analysis of a two-patch model with Allee effect and dispersal