In Bifurcations, Symmetry and Patterns (eds. J. Buescu, S.B.S.D. Castro, A.P.S. Dias and I.S. Labouriau) Birkhauser: Basel (2003) 101-114.

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

A.M. Rucklidge
Department of Applied Mathematics,
University of Leeds, Leeds, LS2 9JT

M. Silber.
Department of Engineering Sciences and Applied Mathematics,
Northwestern University, Evanston, IL 60208, USA

J. Fineberg
The Racah Institute of Physics,
The Hebrew University of Jerusalem,
Givat Ram, Jerusalem 91904 Israel

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 analyse the bifurcations involved in creating the three new patterns using a symmetry-based approach. Each of the three examples reveals a different situation that can arise in the theoretical analysis.



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