Hierarchical Abstraction of Phase Response Curves of Synchronized   Systems of Coupled Oscillators
  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. 
Jaijeet Roychowdhury
nlin.CD math.DS q-bio.QM