Networks on the edge of chaos: global feedback control of turbulence in oscillator networks.

Random networks of coupled phase oscillators with phase shifts in the interaction functions are considered. In such systems, extensive chaos (turbulence) is observed in a wide range of parameters. We show that, by introducing global feedback, the turbulence can be suppressed and a transition to synchronous oscillations can be induced. Our attention is focused on the transition scenario and the properties of patterns, including intermittent turbulence, which are found at the edge of chaos. The emerging coherent patterns represent various self-organized active (sub)networks whose size and behavior can be controlled.