A Mathematical Model for the Propagation of an Animal Species on a Plain

A mathematical model for the dynamics of an animal species propagating on a plain is constructed. Travelling wave solutions are then sought for two cases, the case with constant diffusion coefficient and that with density-dependent diffusion coefficient. The results show the existence of travelling wave solutions in both cases. The existence of travelling wave solutions for the two-dimensional model is important as it captures more realistically the physical interactions of species in a habitat. The minimum wave speeds as well as the basins of attraction were determined. The results also indicate the occurrence of a saddle-node bifurcation in the case with density-dependent diffusion coefficient. The basins of attraction in both cases are functions of the wave speed and is still a subject for further investigation.