  We prove that a group of injection-locked oscillators, each modelled using a
nonlinear phase macromodel, responds as a single oscillator to small external
perturbations. More precisely, we show that any group of injection-locked
oscillators has a single effective PRC [1] or PPV [2], [3] that characterises
its phase/timing response to small external perturbations. This result
constitutes a foundation for understanding and predicting
synchronization/timing hierarchically in large, complex systems that arise in
nature and engineering.
