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| In joint work with M. Golubitsky (Bifurcations from Synchrony in Homogeneous Networks: Linear Theory, SIADS 8,40-75 (2009)) we investigated the generic structure of the linearization of the vectorfield at fully synchronous solutions in regular networks. Independent of the symmetry properties of the network the results show a structural similarity to the linearization of equivariant systems at fully symmetric solutions. These results have implications which allow statements similar to the equivariant branching lemma. \\
Here, we want to follow this approach further and show that some bifurcation results which are known for (certain) equivariant systems remain true in the context of regular networks. |
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