Analytical Phase Reduction for Weakly Nonlinear Oscillators

TL;DR

This paper develops an analytical method for phase reduction of weakly nonlinear oscillators using Poincaré-Lindstedt perturbation theory, enabling better understanding of synchronization in complex oscillator ensembles.

Contribution

It introduces a generalized analytical phase reduction technique applicable to a broad class of oscillators, extending beyond specific systems.

Findings

Analytical phase models accurately predict synchronization behavior.

Application to Van der Pol oscillators demonstrates the method's effectiveness.

Provides a new tool for studying collective dynamics in nonlinear oscillators.

Abstract

Phase reduction is a dimensionality reduction scheme to describe the dynamics of nonlinear oscillators with a single phase variable. While it is crucial in synchronization analysis of coupled oscillators, analytical results are limited to few systems. In this letter, we analytically perform phase reduction for a wide class of oscillators by extending the Poincar\'e-Lindstedt perturbation theory. We exemplify the utility of our approach by analyzing an ensemble of Van der Pol oscillators, where the derived phase model provides analytical predictions of their collective synchronization dynamics