# Phase description of chaotic oscillators

## TL;DR

This paper introduces a phase description method for chaotic oscillators that includes non-phase dynamics, improving understanding and characterization of chaotic phase synchronization in systems like Rössler and Lorenz oscillators.

## Contribution

It systematically incorporates non-phase variables into the phase description, enhancing the qualitative analysis of chaotic phase synchronization.

## Key findings

- Accurately describes distorted synchronization regions
- Validates the method on Rössler and Lorenz oscillators
- Identifies origins of synchronization region distortions

## Abstract

This paper presents a phase description of chaotic dynamics for the study of chaotic phase synchronization. A prominent feature of the proposed description is that it systematically incorporates the dynamics of the non-phase variables inherent in the system. Taking these non-phase dynamics into account is essential for capturing the complicated nature of chaotic phase synchronization, even in a qualitative manner. We numerically verified the validity of the proposed description in application to the R\"{o}ssler and Lorenz oscillators, and we found that our method provides an accurate description of the characteristic distorted shapes of the synchronization regions for these chaotic oscillators. Furthermore, the proposed description allows us to systematically identify and describe the origin of this distortion.