Pulse Dynamics in a Bistable Reaction-Diffusion System with Chemotaxis

Abstract

We consider pulse dynamics in a bistable reaction-diffusion system with chemotaxis. We derive the ordinary differential equation of interfaces by applying the multiple scales method to the reaction-diffusion system for examining the effect of the chemotaxis on pulse dynamics in one dimension. The stability of the standing pulse is considered by two different methods, and the applicability of the methods is demonstrated. The chemotaxis influences the Hopf and drift bifurcations and the collision of two traveling pulses. It also enlarges the bifurcation point and enhances the repulsive force between pulses so that the parameter region of the elastic collision becomes large. Although the ordinary differential equation of interfaces can describe the elastic collision, it cannot describe the pair annihilation of pulses caused by the collision. The conditions for the reliable calculation of pulse collision are discussed.