From localized spot to the formation of invaginated labyrinth structures in spatially extended systems

TL;DR

This paper investigates how localized spots in a spatial system can deform and evolve into complex labyrinth structures through instabilities, using a variational Swift-Hohenberg model.

Contribution

It provides a detailed analysis of the conditions leading to shape transformations from spots to labyrinths in a theoretical model.

Findings

Circular spots become elliptical under certain conditions.

Elongated structures develop transversal instabilities.

Labyrinth structures invade the entire space.

Abstract

The stability of a circular localized spot with respect to azimuthal perturbations is studied in in a variational Swift-Hohenberg model equation. The conditions under which the circular shape undergoes an elliptical deformation that transform it into a rod shape structure are analyzed. As it elongates the rod-like structure exhibits a transversal instability that generates an invaginated labyrinth structure which invades all the space available.