# Nonlinear phase coupling functions: a numerical study

## TL;DR

This paper investigates higher-order nonlinear phase coupling functions in forced oscillators, specifically the Stuart-Landau model, demonstrating their effectiveness in predicting synchronization regions beyond first-order approximations.

## Contribution

It introduces a numerical analysis of phase coupling functions up to the fourth order, extending the understanding of phase reduction in forced oscillators.

## Key findings

- Nonlinear phase coupling functions accurately predict synchronization regions.
- Higher-order coupling functions provide better approximations than first-order.
- Numerical methods effectively analyze complex phase interactions.

## Abstract

Phase reduction is a general tool widely used to describe forced and interacting self-sustained oscillators. Here we explore the phase coupling functions beyond the usual first-order approximation in the strength of the force. Taking the periodically forced Stuart-Landau oscillator as the paradigmatic model, we determine and numerically analyse the coupling functions up to the fourth order in the force strength. We show that the found nonlinear phase coupling functions can be used for predicting synchronization regions of the forced oscillator.