# Emergence of second coherent regions for breathing chimera states

## TL;DR

This paper investigates breathing chimera states in nonlocally coupled oscillators, identifying two types and analyzing their transition, with a new self-consistent method to understand their local coherence patterns.

## Contribution

It introduces a classification of breathing chimeras into two types and develops a self-consistent analysis applicable to these states.

## Key findings

- Identification of two distinct breathing chimera types.
- Demonstration of transition from type I to type II with increased amplitude.
- Development of a new analytical approach for local order parameters.

## Abstract

Chimera states in one-dimensional nonlocally coupled phase oscillators are mostly assumed to be stationary, but breathing chimeras can occasionally appear, branching from the stationary chimeras via Hopf bifurcation. In this paper, we demonstrate two types of breathing chimeras: The type I breathing chimera looks the same as the stationary chimera at a glance, while the type II consists of multiple coherent regions with different average frequencies. Moreover, it is shown that the type I changes to the type II by increasing the breathing amplitude. Furthermore, we develop a self-consistent analysis of the local order parameter, which can be applied to breathing chimeras, and numerically demonstrate this analysis in the present system.