From coupled networks of systems to networks of states in phase space

This is the author accepted manuscript. The final version is available from American Institute of Mathematical Sciences (AIMS) via the DOI in this record.Dynamical systems on graphs can show a wide range of behaviours beyond simple synchronization - even simple globally coupled structures can exhibit attractors with intermittent and slow switching between patterns of synchrony. Such attractors, called heteroclinic networks, can be well described as networks in phase space and in this paper we review some results and examples of how these robust attractors can be characterised from the synchrony properties as well how coupled systems can be designed to exhibit given but arbitrary network attractors in phase space