Collective Phase Sensitivity

TL;DR

This paper develops a theoretical framework to analyze how populations of interacting oscillators respond collectively to external perturbations, linking microscopic and macroscopic phase sensitivities, and applies it to synchronization phenomena.

Contribution

It introduces a two-step phase reduction method to derive macroscopic phase sensitivity from microscopic oscillator properties, advancing understanding of collective responses.

Findings

Derived a formula for collective phase sensitivity in globally-coupled oscillators.

Quantified stability of noise-induced synchronization between oscillator populations.

Validated the approach through application to collective oscillation scenarios.

Abstract

The collective phase response to a macroscopic external perturbation of a population of interacting nonlinear elements exhibiting collective oscillations is formulated for the case of globally-coupled oscillators. The macroscopic phase sensitivity is derived from the microscopic phase sensitivity of the constituent oscillators by a two-step phase reduction. We apply this result to quantify the stability of the macroscopic common-noise induced synchronization of two uncoupled populations of oscillators undergoing coherent collective oscillations.