Hierarchical Abstraction of Nonlinear Oscillator Macromodels

摘要

In this work, we prove that a group of injection-locked oscillators, each described by a PPV phase macromodel, responds as a single oscillator to external inputs; i.e., that any group of injection-locked oscillators has a single effective PPV that characterises its response to external inputs. This result provides a firm mathematical foundation for understanding and predicting synchronization/timing hierarchically in large, complex systems of interacting oscillators that arise in engineering and nature - potentially explaining, for example, fascinating empirical measurements of rat and human responses to light stimuli [4].