Splitting instability of cellular structures in the Ginzburg-Landau model under the feedback control

TL;DR

This paper investigates the splitting instability of cellular structures in a Ginzburg-Landau model, using feedback control to manipulate interface length and analyze bifurcation behavior through numerical simulations and coupled mode equations.

Contribution

It introduces a feedback control method to study cellular splitting in the Ginzburg-Landau model and analyzes the bifurcation structure of the instability.

Findings

Cellular structures deform and split as interface length increases.

Feedback control effectively induces and studies splitting instability.

Coupled mode equations reveal the bifurcation structure of the process.

Abstract

We study numerically a Ginzburg-Landau type equation for micelles in two dimensions. The domain size and the interface length of a cellular structure are controlled by two feedback terms. The deformation and the successive splitting of the cellular structure are observed when the controlled interface length is increased. The splitting instability is further investigated using coupled mode equations to understand the bifurcation structure.