Diversity of dynamical behaviors due to initial conditions: Extension of the Ott-Antonsen ansatz for identical Kuramoto-Sakaguchi phase oscillators

Akihisa Ichiki and Keiji Okumura

Phys. Rev. E 101, 022211 – Published 18 February 2020

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, an 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.

Received 5 November 2019
Accepted 3 February 2020

DOI:https://doi.org/10.1103/PhysRevE.101.022211

Physics Subject Headings (PhySH)

Chimera states Coupled oscillators Synchronization Synchronization transition

Nonlinear Dynamics

Authors & Affiliations

Akihisa Ichiki ^1,* and Keiji Okumura ^2,†

¹Institutes of Innovation for Future Society, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan
²Institute of Economic Research, Hitotsubashi University, Kunitachi, Tokyo 186-8603, Japan

^*ichiki@chem.material.nagoya-u.ac.jp
^†kokumura@ier.hit-u.ac.jp

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Vol. 101, Iss. 2 — February 2020

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Physical Review E

covering statistical, nonlinear, biological, and soft matter physics