(III) Coupled cell networks and synchrony-breaking bifurcations

In the third part, we extend this method of equivariant degree to the realm of coupled cell networks, which are (generally non-symmetric) networks of dynamical systems, where the time evolution of one system is influenced by others. Under the general framework of coupled cell networks, we apply the newly defined ``lattice equivariant degree'' to studying synchrony-breaking bifurcations, a local bifurcation through which a fully synchronous equilibrium loses its stability and bifurcates to states of less synchrony in space.