Deformation of a self-propelled domain in an excitable reaction-diffusion system

TL;DR

This paper develops a theoretical framework for understanding how self-propelled domains in excitable reaction-diffusion systems deform and change motion patterns as their velocity increases, revealing bifurcation phenomena.

Contribution

It introduces a new set of equations describing the deformation and motion of self-propelled domains, including shape bifurcations, in excitable reaction-diffusion systems.

Findings

Deformation from circular shape occurs with increased velocity.

Bifurcation from straight to circular motion is identified.

Derived equations predict steady shapes and motion transitions.

Abstract

We formulate the theory for a self-propelled domain in an excitable reaction-diffusion system in two dimensions where the domain deforms from a circular shape when the propagation velocity is increased. In the singular limit where the width of the domain boundary is infinitesimally thin, we derive a set of equations of motion for the center of gravity and two fundamental deformation modes. The deformed shapes of a steadily propagating domain are obtained. The set of time-evolution equations exhibits a bifurcation from a straight motion to a circular motion by changing the system parameters.