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Symmetry and synchrony in coupled cell networks 3 : exotic patterns

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Antoneli, Fernando and Stewart, Ian. (2008) Symmetry and synchrony in coupled cell networks 3 : exotic patterns. International Journal of Bifurcation and Chaos, Vol.18 (No.2). pp. 363-373. ISSN 0218-1274

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Official URL: http://dx.doi.org/10.1142/S0218127408020331

Abstract

This paper continues the study of patterns of synchrony ( equivalently, balanced colorings or flowinvariant subspaces) in symmetric coupled cell networks, and their relation to fixed-point spaces of subgroups of the symmetry group. Our aim is to provide a group-theoretic explanation of the "exotic" balanced coloring previously discussed in Part 2. Here we show that the pattern can be obtained as a projection into two dimensions of a fixed-point pattern in a three-dimensional lattice. We prove a general theorem giving sufficient conditions for such a construction to lead to a balanced coloring, for an arbitrary direct product of group networks.

Item Type:

Journal Article

Subjects:

Q Science > Q Science (General)
Q Science > QA Mathematics

Divisions:

Faculty of Science > Mathematics

Library of Congress Subject Headings (LCSH):

System theory, Group theory, Symmetry groups, Symmetry (Physics), Chaotic behavior in systems, Pattern formation (Physical sciences)

Journal or Publication Title:

International Journal of Bifurcation and Chaos

Publisher:

World Scientific Publishing Co. Pte. Ltd.

ISSN:

0218-1274

Official Date:

February 2008

Dates:

Date	Event
February 2008	Published

Volume:

Vol.18

Number:

No.2

Number of Pages:

Page Range:

pp. 363-373

Identification Number:

DOI:10.1142/S0218127408020331

Status:

Peer Reviewed

Publication Status:

Published

Access rights to Published version:

Restricted or Subscription Access

Funder:

National Science Foundation (U.S.) (NSF), Engineering and Physical Sciences Research Council (EPSRC), Universidade do Porto. Centro de Matemática (CMUP), Fundação para a Ciência e a Tecnologia (FCT)

Grant number:

DMS-0244529 (NSF)

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