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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. doi:DOI:10.1142/S0218127408020331
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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 |
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| 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: |
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| Volume: | Vol.18 | ||||
| Number: | No.2 | ||||
| Number of Pages: | 11 | ||||
| Page Range: | pp. 363-373 | ||||
| DOI: | 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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