Steady-state bifurcations for three-cell networks with asymmetric inputs

We consider codimension-one steady-state bifurcations for coupled cell networks with identical cells and asymmetric inputs. We obtain general results both for networks with any number of cells and any number of asymmetric inputs covering in particular networks with three cells. These results rely on the eigenvalue structure and the existence, or not, of synchrony subspaces. We describe the lattices of synchrony subspaces annotated with the network eigenfunctions for networks with three cells. Applying the previous results, we classify the synchrony-breaking bifurcations that can occur for three-cell minimal networks with one, two or six asymmetric inputs.

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