The spreading speed of single-species models with resource-dependent dispersal and a free boundary

Abstract

In this paper, we study the spreading speed of single-species models with resource-dependent dispersal and a free boundary, which describe the propagation process of an invasive species in a spatially heterogeneous environment. To overcome the analytical difficulties brought by the resource-dependent dispersal, we use an idea of changing variables to transform the above models into the uniform dispersal ones. Then estimates of spreading speed are obtained by a semi-wave problem. Compared to the free boundary problems with random dispersal, the spreading speed not only depends on the resource-dependent dispersal but also increases in it.