Buckling of scroll waves

TL;DR

This paper investigates how scroll waves in thin excitable media can become unstable and buckle into a precessing state as the medium's thickness increases, leading to turbulence, supported by a simplified theoretical model and numerical simulations.

Contribution

It introduces a simplified theory explaining the buckling transition of scroll waves due to filament rigidity and medium thickness, supported by numerical examples.

Findings

Scroll waves can buckle and become unstable as medium thickness increases.

Filament rigidity stabilizes scroll waves in thin layers.

Thicker layers lead to meandering and turbulence of scroll waves.

Abstract

A scroll wave in a sufficiently thin layer of an excitable medium with negative filament tension can be stable nevertheless due to filament rigidity. Above a certain critical thickness of the medium, such scroll wave will have a tendency to deform into a buckled, precessing state. Experimentally this will be seen as meandering of the spiral wave on the surface, the amplitude of which grows with the thickness of the layer, until a break-up to scroll wave turbulence happens. We present a simplified theory for this phenomenon and illustrate it with numerical examples.