Diversity of dynamical behaviors due to initial conditions: exact results with extended Ott--Antonsen ansatz for identical Kuramoto--Sakaguchi phase oscillators
arXiv:1911.06112 · doi:10.1103/PhysRevE.101.022211
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.
arXiv comment4 figures
References in corpus (11)
- Chimera States for Coupled Oscillators
- Long Time Evolution of Phase Oscillator Systems
- Exact Results for the Kuramoto Model with a Bimodal Frequency Distribution
- Phase oscillators with global sinusoidal coupling evolve by Mobius group action
- Stability diagram for the forced Kuramoto model
- Noise-Induced Synchronization of a Large Population of Globally Coupled Nonidentical Oscillators
- Linear Stability and the Braess Paradox in Coupled Oscillators Networks and Electric Power Grids
- Phase synchronization between collective rhythms of globally coupled oscillator groups: noiseless non-identical case
- Collective mode reductions for populations of coupled noisy oscillators
- Repulsively Coupled Kuramoto-Sakaguchi Phase Oscillators Ensemble Subject to Common Noise
- Kuramoto model with coupling through an external medium