UNSPECIFIED (1996) Coupled cells with internal symmetry .2. Direct products. NONLINEARITY, 9 (2). pp. 575-599. ISSN 0951-7715

Full text not available from this repository.

Abstract

We continue the study of arrays of coupled identical cells that possess both global and internal symmetries, begun in part I. Here we concentrate on the 'direct product' case, for which the symmetry group of the system decomposes as the direct product L x g of the internal group L and the global group g. Again, the main aim is to find general existence conditions for symmetry-breaking steady-state and Hopf bifurcations by reducing the problem to known results for systems with symmetry L or g separately. Unlike the wreath product case, the theory makes extensive use of the representation theory of compact Lie groups. Again the central algebraic task is to classify axial and C-axial subgroups of the direct product and to relate them to axial and C-axial subgroups of the two groups L and g. We demonstrate how the results lead to efficient classification by studying both steady state and Hopf bifurcation in rings of coupled cells, where L = O(2) and g = D-n. In particular we show that for Hopf bifurcation the case n = 4 module 4 is exceptional, by exhibiting two extra types of solution that occur only for those values of n.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics Q Science > QC Physics
Journal or Publication Title:	NONLINEARITY
Publisher:	IOP PUBLISHING LTD
ISSN:	0951-7715
Date:	March 1996
Volume:	9
Number:	2
Number of Pages:	25
Page Range:	pp. 575-599
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/18874

Data sourced from Thomson Reuters' Web of Knowledge

Request changes to a record

Actions (login required)

View Item