title: Rotation sets for networks of circle maps.
abstract: 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.
authors.affiliation: Department of Mathematics, University of Houston, Houston, Texas 77204-3008, USA. parwani@math.uh.edu
authors.forename: Kamlesh
authors.initials: K
authors.lastname: Parwani
authors.forename: Kresimir
authors.initials: K
authors.lastname: Josić