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- Title
FORMATION, STABILITY AND BASIN OF PHASE-LOCKING FOR KURAMOTO OSCILLATORS BIDIRECTIONALLY COUPLED IN A RING.
- Authors
Zhao, Xiaoxue; Li, Zhuchun; Xue, Xiaoping
- Abstract
We consider the dynamics of bidirectionally coupled identical Kuramoto oscillators in a ring, where each oscillator is inuenced 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 Lojasiewicz inequality.
- Subjects
RING theory; PARAMETRONS; STABILITY theory; STOCHASTIC convergence; MATHEMATICAL inequalities; ESTIMATION theory
- Publication
Networks & Heterogeneous Media, 2018, Vol 13, Issue 2, p323
- ISSN
1556-1801
- Publication type
Article
- DOI
10.3934/nhm.2018014