Diversity of dynamical behaviors due to initial conditions: exact results with extended Ott--Antonsen ansatz for identical Kuramoto--Sakaguchi phase oscillators

TL;DR

This paper extends the Ott--Antonsen ansatz to better analyze the diverse dynamical behaviors of identical Kuramoto--Sakaguchi oscillators arising from different initial conditions, revealing new cluster and chimera-like states.

Contribution

A systematic extension of the Ott--Antonsen ansatz is introduced to relax initial condition restrictions, enabling analysis of a broader range of behaviors in coupled oscillators.

Findings

The extended ansatz captures cluster and chimera-like solutions.

It accurately approximates behaviors for arbitrary initial conditions.

New dynamical states are identified beyond conventional analysis.

Abstract

The Ott--Antonsen ansatz is a powerful tool to extract the behaviors of coupled phase oscillators, but it imposes a strong restriction on the initial condition. Herein, a systematic extension of the Ott--Antonsen ansatz is proposed to relax the restriction, enabling the systematic approximation of the behavior of a globally coupled phase oscillator system with an arbitrary initial condition. The proposed method is validated on the Kuramoto--Sakaguchi model of identical phase oscillators. The method yields cluster and chimera-like solutions that are not obtained by the conventional ansatz.