Chemotactic cellular migration: Smooth and discontinuous travelling wave solutions

Abstract

A simple model of chemotactic cell migration gives rise to travelling wave solutions. By varying the cellular growth rate and chemoattractant production rate, travelling waves with both smooth and discontinuous fronts are found using phase plane analysis. The phase plane exhibits a curve of singularities whose position relative to the equilibrium points in the phase plane determines the nature of the heteroclinic orbits, where they exist. Smooth solutions have trajectories connecting the steady states lying to one side of the singular curve. Travelling shock waves arise by connecting trajectories passing through a special point in the singular curve and recrossing the singular curve, by way ..