High-order phase reduction for coupled 2D oscillators

TL;DR

This paper develops a comprehensive framework for higher-order phase reduction of coupled 2D oscillators, enabling more accurate modeling of finite coupling effects beyond traditional small-coupling assumptions.

Contribution

It introduces a general method to derive higher-order coupling terms for two-dimensional oscillators with arbitrary coupling, extending phase reduction theory.

Findings

Accurately predicts Arnold's tongue for van der Pol oscillator

Demonstrates validity of higher-order phase reduction for finite coupling

Provides a versatile framework applicable to generic 2D oscillators

Abstract

Phase reduction is a general approach to describe coupled oscillatory units in terms of their phases, assuming that the amplitudes are enslaved. For such a reduction, the coupling should be small, but one also expects the reduction to be valid for finite coupling. This paper presents a general framework allowing us to obtain coupling terms in higher orders of the coupling parameter for generic two-dimensional oscillators and arbitrary coupling terms. The theory is illustrated with an accurate prediction of Arnold's tongue for the van der Pol oscillator exploiting higher-order phase reduction.