# Snaking branches of planar BCC fronts in the 3D Brusselator

## TL;DR

This paper investigates complex snaking bifurcation structures of planar fronts in the 3D Brusselator model, revealing localized patterns and transitions between different spatial structures using numerical continuation methods.

## Contribution

It applies advanced numerical bifurcation analysis to the 3D Brusselator, exploring snaking branches and localized solutions between BCCs and tubes, with theoretical insights from Maxwell points.

## Key findings

- Identification of snaking branches of planar fronts
- Approximation of localized BCCs and embedded structures
- Analysis of moving fronts between lamellas and tubes

## Abstract

We present results of the application of the numerical continuation and bifurcation package pde2path to the 3D Brusselator model, focusing on snaking branches of planar fronts between body centered cubes (BCCs) and the spatial homogeneous solution, and on planar fronts between BCCs and tubes (also called square prisms). These solutions also yield approximations of localized BCCs, and of BCCs embedded in a background of tubes (or vice versa). Additionally, we compute some moving fronts between lamellas and tubes. To give some theoretical background, and to aid the numerics for the full system, we use the Maxwell points for the cubic amplitude system over the BCC lattice.