Drift Laws for Spiral Waves on Curved Anisotropic Surfaces

TL;DR

This paper develops a quantitative theory linking the Ricci curvature scalar of curved surfaces to the drift behavior of spiral waves in excitable systems like chemical reactions and cardiac tissue.

Contribution

It introduces explicit equations for spiral wave drift, direction, and period based on surface curvature, applicable to diverse anisotropic systems.

Findings

Drift direction depends on Ricci scalar curvature extrema.

Numerical simulations confirm theoretical predictions.

Applicable to chemical and biological excitable media.

Abstract

Rotating spiral waves organize spatial patterns in chemical, physical and biological excitable systems. Factors affecting their dynamics such as spatiotemporal drift are of great interest for par- ticular applications. Here, we propose a quantitative description for spiral wave dynamics on curved surfaces which shows that for a wide class of systems, including the BZ reaction and anisotropic cardiac tissue, the Ricci curvature scalar of the surface is the main determinant of spiral wave drift. The theory provides explicit equations for spiral wave drift direction, drift velocity and the period of rotation. Depending on the parameters, the drift can be directed to the regions of either maximal or minimal Ricci scalar curvature, which was verified by direct numerical simulations.