SYMMETRY AND SYNCHRONY IN COUPLED CELL NETWORKS 3
2008 ◽
Vol 18
(02)
◽
pp. 363-373
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Keyword(s):
This paper continues the study of patterns of synchrony (equivalently, balanced colorings or flow-invariant 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.
2006 ◽
Vol 16
(03)
◽
pp. 559-577
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2007 ◽
Vol 17
(03)
◽
pp. 935-951
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Keyword(s):
1985 ◽
Vol 107
(1)
◽
pp. 70-76
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Keyword(s):
1990 ◽
Vol 48
(3)
◽
pp. 166-167
Keyword(s):