Local bifurcation in symmetric coupled cell networks: Linear theory

We focus on the analysis of the linearized vector field at a fully symmetric equilibrium and show that in the case of active cells, if Γ is Abelian the network structure does not influence the types of codimension one local bifurcations. We also show that beyond this context, when Γ is not Abelian, cells are passive, or when considering local bifurcations of higher codimensions, anomalies due to the network structure may arise.