Dynamic networks at the edge of chaos

A network of coupled phase oscillators is considered. Interactions between the oscillators are characterized by phase shifts, effectively taking into account interaction delays. We show that in this simple model coherent collective dynamics can emerge. Alternatively, chaos can develop when interaction phase shifts are large enough. Introducing a global feedback, chaotic behavior can be suppressed, giving rise to localized structures in the network with complex dynamical behavior. This transition scenario is analyzed, and special attention is paid to the dynamical properties of self-organized structures.