Secondary instabilities of hexagons: a bifurcation analysis of experimentally observed Faraday wave patterns

Abstract

We examine three experimental observations of Faraday waves generated by two-frequency forcing, in which a primary hexagonal pattern becomes unstable to three different superlattice patterns. We use the symmetry-based approach developed by Tse et al. to analyse the bifurcations involved in creating the three new patterns. Each of the three examples reveals a different situation that can arise in the theoretical analysis.