Evolution of the Spiral Waves in Excitable System

TL;DR

This paper uses topological current theory to analyze the evolution, generation, annihilation, and interaction of spiral waves in two-dimensional excitable systems, providing a topological framework for understanding their dynamics.

Contribution

It introduces a topological approach to study spiral wave dynamics, revealing how they generate, annihilate, and interact through topological charge and bifurcation points.

Findings

Spiral waves can generate or annihilate at limit points.

Spiral waves encounter, split, or merge at bifurcation points.

Topological properties govern the evolution of spiral waves.

Abstract

Spiral wave, whose rotation center can be regarded as a point defect, widely exists in various two dimensional excitable systems. In this paper, by making use of \emph{Duan's topological current theory}, we obtain the charge density of spiral waves and the topological inner structure of its topological charge. The evolution of spiral wave is also studied from the topological properties of a two-dimensional vector field. The spiral waves are found generating or annihilating at the limit points and encountering, splitting, or merging at the bifurcation points of the two-dimensional vector field. Some applications of our theory are also discussed.