{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,6,20]],"date-time":"2024-06-20T21:15:54Z","timestamp":1718918154256},"reference-count":23,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2006,3]]},"abstract":" Equivariant dynamical systems possess canonical flow-invariant subspaces, the fixed-point spaces of subgroups of the symmetry group. These subspaces classify possible types of symmetry-breaking. Coupled cell networks, determined by a symmetry groupoid, also possess canonical flow-invariant subspaces, the balanced polydiagonals. These subspaces classify possible types of synchrony-breaking, and correspond to balanced colorings of the cells. A class of dynamical systems that is common to both theories comprises networks that are symmetric under the action of a group \u0393 of permutations of the nodes (\"cells\"). We investigate connections between balanced polydiagonals and fixed-point spaces for such networks, showing that in general they can be different. In particular, we consider rings of ten and twelve cells with both nearest and next-nearest neighbor coupling, showing that exotic balanced polydiagonals \u2014 ones that are not fixed-point spaces \u2014 can occur for such networks. We also prove the \"folk theorem\" that in any \u0393-equivariant dynamical system on Rk<\/jats:sup> the only flow-invariant subspaces are the fixed-point spaces of subgroups of \u0393. <\/jats:p>","DOI":"10.1142\/s0218127406015167","type":"journal-article","created":{"date-parts":[[2006,5,23]],"date-time":"2006-05-23T07:19:24Z","timestamp":1148368764000},"page":"559-577","source":"Crossref","is-referenced-by-count":31,"title":["SYMMETRY AND SYNCHRONY IN COUPLED CELL NETWORKS 1: FIXED-POINT SPACES"],"prefix":"10.1142","volume":"16","author":[{"given":"FERNANDO","family":"ANTONELI","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics, University of S\u00e3o Paulo, S\u00e3o Paulo SP 05508-090, Brazil"}]},{"given":"IAN","family":"STEWART","sequence":"additional","affiliation":[{"name":"Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/18\/5\/016"},{"key":"rf2","author":"Antoneli F.","journal-title":"Int. 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