Formation, stability and basin of phase-locking for Kuramoto oscillators bidirectionally coupled in a ring | Zendy

Xiaoxue Zhao | Zendy; Zhuchun Li | Zendy; Xiaoping Xue | Zendy

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Formation, stability and basin of phase-locking for Kuramoto oscillators bidirectionally coupled in a ring

Author(s) -

Xiaoxue Zhao,

Zhuchun Li,

Xiaoping Xue

Publication year - 2018

Publication title -

networks and heterogeneous media

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.732

H-Index - 34

eISSN - 1556-181X

pISSN - 1556-1801

DOI - 10.3934/nhm.2018014

Subject(s) - kuramoto model , phase locking , ring (chemistry) , instability , convergence (economics) , stability (learning theory) , synchronization networks , phase (matter) , control theory (sociology) , synchronization (alternating current) , physics , dynamics (music) , work (physics) , rate of convergence , mathematics , statistical physics , topology (electrical circuits) , mechanics , computer science , quantum mechanics , telecommunications , chemistry , combinatorics , artificial intelligence , economic growth , acoustics , control (management) , machine learning , organic chemistry , economics , channel (broadcasting)

We consider the dynamics of bidirectionally coupled identical Kuramoto oscillators in a ring, where each oscillator is influenced sinusoidally by two neighboring oscillator. Our purpose is to understand its dynamics in the following aspects: 1. identify all the phase-locked states (or equilibria) with stability or instability; 2. estimate the basins for stable phase-locked states; 3. identify the convergence rate towards phase-locked states. The crucial tool in this work is the celebrated theory of Łojasiewicz inequality.

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