A three-scale model of spatio-temporal bursting

TL;DR

This paper investigates spatio-temporal bursting phenomena in a three-scale reaction-diffusion model, revealing how different scale separations lead to traveling or standing bursts, governed by the winged cusp singularity and its bifurcation structure.

Contribution

It introduces a three-scale reaction-diffusion model organized by the winged cusp singularity, linking burst behaviors to bifurcation diagrams and universal unfoldings.

Findings

Large time-scale separation yields traveling bursts.

Large space-scale separation results in standing bursts.

Burst modulation corresponds to paths in the winged-cusp unfolding.

Abstract

We study spatio-temporal bursting in a three-scale reaction diffusion equation organized by the winged cusp singularity. For large time-scale separation the model exhibits traveling bursts, whereas for large space-scale separation the model exhibits standing bursts. Both behaviors exhibit a common singular skeleton, whose geometry is fully determined by persistent bifurcation diagrams of the winged cusp. The modulation of spatio-temporal bursting in such a model naturally translates into paths in the universal unfolding of the winged-cusp.