M.A.D. Aguiar, A.P.S. Dias, M. Golubitsky and M.C.A. Leite
Homogeneous coupled cell networks with S_3-symmetric quotient
Discrete and Continuous Dynam. Sys. Supplement (2007) 1-9.
In this paper we consider homogeneous networks admitting an S_3-symmetric quotient network. We assume that a codimension-one synchrony-breaking bifurcation from a synchronous equilibrium occurs for that quotient network. We aim to investigate, for different networks admitting that S_3-symmetric quotient, if the degeneracy condition leading to that bifurcation gives rise to branches of steady-state solutions outside the flow-invariant subspace associated with the quotient network. We illustrate that the existence of new solutions can be justified directly or not by the symmetry of the original network. The bifurcation analysis of a six-cell asymmetric network suggests that the existence of new solutions outside the flow-invariant subspace associated with the quotient is `forced' by the symmetry of a five-cell quotient network.