Parker, M. J., Gomes, M. G. M. and Stewart, Ian, 1945-. (2009) Examples or forced symmetry-breaking to heteroclinic cycles and networks in three-dimensional euclidean-invariant systems. International Journal of Bifurcation and Chaos, Vol.19 (No.5). pp. 1655-1678. ISSN 0218-1274

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Abstract

In [Parker et al., 2008a] group theory was employed to prove the existence of homoclinic cycles in forced symmetry-breaking of simple (SC), face-centered (FCC), and body-centered (BCC) cubic planforms. In this paper we extend this classification demonstrating that more elaborate heteroclinic cycles and networks can arise through the same process. Our methods naturally generate graphs that represent possible heteroclinic cycles and networks. The results do not depend on the representation of the symmetry group and are thus quite general. This study is motivated by pattern formation in three dimensions which occur in reaction diffusion systems, certain nonlinear optical systems and the polyacrylamide methylene blue oxygen reaction. This work extends previous work by Parker et al. [2006, 2008a, 2008b] and Hou and Golubitsky [1997].

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics Q Science
Divisions:	Faculty of Science > Mathematics
Journal or Publication Title:	International Journal of Bifurcation and Chaos
Publisher:	World Scientific Publishing Co. Pte. Ltd.
ISSN:	0218-1274
Date:	May 2009
Volume:	Vol.19
Number:	No.5
Number of Pages:	24
Page Range:	pp. 1655-1678
Identification Number:	10.1142/S0218127409023767
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Funder:	Engineering and Physical Sciences Research Council (EPSRC)
URI:	http://wrap.warwick.ac.uk/id/eprint/17429

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