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

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.

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References in corpus (4)

• Exact Results for the Kuramoto Model with a Bimodal Frequency Distribution
• Stability diagram for the forced Kuramoto model
• Noise-Induced Synchronization of a Large Population of Globally Coupled Nonidentical Oscillators
• Phase synchronization between collective rhythms of globally coupled oscillator groups: noiseless non-identical case

Cited by in corpus (1)

• Exact finite-dimensional reduction for a population of noisy oscillators and its link to Ott-Antonsen and Watanabe-Strogatz theories