We consider continuous maps of the torus, homotopic to the identity, that arise from systems of coupled circle maps and discuss the relationship between network architecture and rotation sets. Our main result is that when the map on the torus is invertible, network architecture can force the set of rotation vectors to lie in a low-dimensional subspace. In particular, the rotation set for an all-to-all coupled system of identical cells must be a subset of a line.
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Research Article| March 31 2006
Rotation sets for networks of circle maps
Kamlesh Parwani, Krešimir Josić; Rotation sets for networks of circle maps. Chaos 1 March 2006; 16 (1): 015115. https://doi.org/10.1063/1.2146114
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