dorsal/arxiv
View SchemaSynchronization of globally-coupled phase oscillators: singularities and scaling for general couplings
| Authors | John David Crawford, K. T. R. Davies |
|---|---|
| Categories | |
| ArXiv ID | patt-sol/9701006 |
| URL | https://arxiv.org/abs/patt-sol/9701006 |
Abstract
The onset of collective behavior in a population of globally coupled oscillators with randomly distributed frequencies is studied for phase dynamical models with arbitrary coupling; the effect of a stochastic temporal variation in the frequencies is also included. The Fokker-Planck equation for the coupled Langevin system is reduced to a kinetic equation for the oscillator distribution function. Instabilities of the phase-incoherent state are studied by center manifold reduction to the amplitude dynamics of the unstable modes. Depending on the coupling, the coefficients in the normal form can be singular in the limit of weak instability when the diffusive effect of the noise is neglected. A detailed analysis of these singularities to all orders in the normal form expansion is presented. Physically, the singularities are interpreted as predicting an altered scaling of the entrained component near the onset of synchronization.
{
"annotation_id": "a0509898-2983-4817-84ce-0c629819b5cb",
"date_created": "2026-03-02T18:00:28.852000Z",
"date_modified": "2026-03-02T18:00:28.852000Z",
"file_hash": "09d29ab726352a62120a37a66ad7e8d5b34563852542021fe3872d1717026e95",
"private": false,
"record": {
"abstract": "The onset of collective behavior in a population of globally coupled\noscillators with randomly distributed frequencies is studied for phase\ndynamical models with arbitrary coupling; the effect of a stochastic temporal\nvariation in the frequencies is also included. The Fokker-Planck equation for\nthe coupled Langevin system is reduced to a kinetic equation for the oscillator\ndistribution function. Instabilities of the phase-incoherent state are studied\nby center manifold reduction to the amplitude dynamics of the unstable modes.\nDepending on the coupling, the coefficients in the normal form can be singular\nin the limit of weak instability when the diffusive effect of the noise is\nneglected. A detailed analysis of these singularities to all orders in the\nnormal form expansion is presented. Physically, the singularities are\ninterpreted as predicting an altered scaling of the entrained component near\nthe onset of synchronization.",
"arxiv_id": "patt-sol/9701006",
"authors": [
"John David Crawford",
"K. T. R. Davies"
],
"categories": [
"patt-sol",
"cond-mat",
"nlin.PS"
],
"title": "Synchronization of globally-coupled phase oscillators: singularities and scaling for general couplings",
"url": "https://arxiv.org/abs/patt-sol/9701006"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "b5eee7b3-e512-4814-9542-049837edb629",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}