Colonies of threaded rings in excitable media

TL;DR

This paper investigates the dynamics and interactions of 'thrings'—a novel spiral wave phenomenon in excitable media—using numerical simulations, revealing stable pairs, wave emission effects, and a frozen nonequilibrium colony state.

Contribution

It provides the first detailed analysis of thrings' collective behavior, interaction mechanisms, and long-term colony evolution in excitable media.

Findings

Attraction leads to stable thring pairs.

Pairs emit higher frequency waves, preventing triplet formation.

Colony evolves into a frozen state of pairs and isolated thrings.

Abstract

A thring is a recent addition to the zoo of spiral wave phenomena found in excitable media and consists of a scroll ring that is threaded by a pair of counter-rotating scroll waves. This arrangement behaves like a particle that swims through the medium. Here, we present the first results on the dynamics, interaction and collective behaviour of several thrings via numerical simulation of the reaction-diffusion equations that model thrings created in chemical experiments. We reveal an attraction between two thrings that leads to a stable bound pair that thwarts their individual locomotion. Furthermore, such a pair emits waves at a higher frequency than a single thring, which protects the pair from the advances of any other thring and rules out the formation of a triplet bound state. As a result, the long-term evolution of a colony of thrings ultimately yields an unusual frozen nonequilibrium state consisting of a collection of pairs accompanied by isolated thrings that are inhibited from further motion by the waves emanating from the pairs.