Coupled Cell Networks: Hopf bifurcation and Interior Symmetry

We consider interior symmetric coupled cell networks where a group of per- mutations of a subset of cells partially preserves the network structure. In this setup, the full analogue of the Equivariant Hopf Theorem for networks with symmetries was obtained by Antoneli, Dias and Paiva (Hopf Bifurcation in Coupled Cell Networks with Interior Symmetries, SIAM J. Appl. Dynam. Sys. (2007) to appear). In this note we present an alternative proof of this result using center manifold reduction.