Travelling front solutions arising in the chemotaxis-growth model

Abstract

We consider a bistable reaction-diffusion-advection system describing the growth of biological individuals which move by diffusion and chemotaxis. We use the singular limit procedure to study the dynamics of growth patterns arising in this system. It is shown that travelling front solutions are transversally stable when the chemotactic effect is weak and, when it becomes stronger, they are destabilized. Numerical simulations reveal that the destabilized solution evolves into complex patterns with dynamic network--like structures.