A Convergence Result for the Kuramoto Model with All-to-All Coupling
- 1 January 2011
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Applied Dynamical Systems
- Vol. 10 (3), 906-920
- https://doi.org/10.1137/090771946
Abstract
We prove a convergence result for the standard Kuramoto model with all-to-all coupling. Specifically,\ud we show that the critical coupling strength associ\ud ated with the onset of completely phase-locked\ud behavior converges in probability as the number of oscillators tends to infinityKeywords
This publication has 9 references indexed in Scilit:
- On Computing the Critical Coupling Coefficient for the Kuramoto Model on a Complete Bipartite GraphSIAM Journal on Applied Dynamical Systems, 2009
- Global Phase-Locking in Finite Populations of Phase-Coupled OscillatorsSIAM Journal on Applied Dynamical Systems, 2008
- The Spectrum of the Partially Locked State for the Kuramoto ModelJournal of Nonlinear Science, 2007
- Singular unlocking transition in the Winfree model of coupled oscillatorsPhysical Review E, 2007
- The spectrum of the locked state for the Kuramoto model of coupled oscillatorsPhysica D: Nonlinear Phenomena, 2005
- The Kuramoto model: A simple paradigm for synchronization phenomenaReviews of Modern Physics, 2005
- Mechanism of Desynchronization in the Finite-Dimensional Kuramoto ModelPhysical Review Letters, 2004
- From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillatorsPhysica D: Nonlinear Phenomena, 2000
- Stability of incoherence in a population of coupled oscillatorsJournal of Statistical Physics, 1991