A framework that measures whether an individual unit (or sub-network) inside a finite dynamical network reproduces its own dynamics when replicated: if a replica driven by the same network synchronizes with its prototype the unit is reliable, and if the replica diverges it is anti-reliable, quantified by the sign of the transversal Lyapunov exponent. Applied to the Kuramoto model of globally coupled phase oscillators it shows that before synchronization onset frequency-central units are reliable while frequency-peripheral units are anti-reliable, with reliability expressible through phase correlations in a fluctuation-dissipation-like relation; sufficiently large sub-networks are always anti-reliable, whereas single units of a recurrent neural network are always reliable.
We consider finite dynamical networks and define internal reliability according to the synchronization properties of a replicated unit or a set of units. If the states of the replicated units coincid…