Hierarchical Abstraction of Phase Response Curves of Synchronized Systems of Coupled Oscillators

TL;DR

This paper demonstrates that groups of injection-locked oscillators can be modeled as a single oscillator with a unified phase response curve, enabling hierarchical analysis of synchronization in complex systems.

Contribution

It proves that synchronized oscillator groups have a single effective PRC or PPV, facilitating hierarchical understanding of their phase response.

Findings

Groups of injection-locked oscillators respond as a single oscillator.

A unified phase response curve characterizes the entire group.

This foundation aids in analyzing large, complex synchronized systems.

Abstract

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.