Abstract:

In this paper, we study the asymptotic dynamics of a single-species model with resource-dependent dispersal in one dimension.

To overcome the analytical difficulties brought by the resource-dependent dispersal, we use the idea of changing variables to transform the model into a uniform dispersal one. Then the existence and uniqueness of positive stationary solution to the model can be verified by the squeezing argument, where the solution plays a crucial role in later analyses. Moreover, the asymptotic behavior of solutions to the model is obtained by the upper-lower solutions method. The result indicates that the solutions of the model converge to the corresponding positive stationary solution locally uniformly in one dimension as time goes to infinity.

Key words: Asymptotic dynamics, Resource-dependent dispersal, Stationary solution, Upper-lower solutions method