dorsal/arxiv
View SchemaAsymptotic description of transients and synchronized states of globally coupled oscillators
| Authors | J. A. Acebron, L. L. Bonilla |
|---|---|
| Categories | |
| ArXiv ID | patt-sol/9706003 |
| URL | https://arxiv.org/abs/patt-sol/9706003 |
| DOI | 10.1016/S0167-2789(97)00197-8 |
Abstract
A two-time scale asymptotic method has been introduced to analyze the multimodal mean-field Kuramoto-Sakaguchi model of oscillator synchronization in the high-frequency limit. The method allows to uncouple the probability density in different components corresponding to the different peaks of the oscillator frequency distribution. Each component evolves toward a stationary state in a comoving frame and the overall order parameter can be reconstructed by combining them. Synchronized phases are a combination of traveling waves and incoherent solutions depending on parameter values. Our results agree very well with direct numerical simulations of the nonlinear Fokker-Planck equation for the probability density. Numerical results have been obtained by finite differences and a spectral method in the particular case of bimodal (symmetric and asymmetric) frequency distribution with or without external field. We also recover in a very easy and intuitive way the only other known analytical results: those corresponding to reflection-symmetric bimodal frequency distributions near bifurcation points.
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"abstract": "A two-time scale asymptotic method has been introduced to analyze the\nmultimodal mean-field Kuramoto-Sakaguchi model of oscillator synchronization in\nthe high-frequency limit. The method allows to uncouple the probability density\nin different components corresponding to the different peaks of the oscillator\nfrequency distribution. Each component evolves toward a stationary state in a\ncomoving frame and the overall order parameter can be reconstructed by\ncombining them. Synchronized phases are a combination of traveling waves and\nincoherent solutions depending on parameter values. Our results agree very well\nwith direct numerical simulations of the nonlinear Fokker-Planck equation for\nthe probability density. Numerical results have been obtained by finite\ndifferences and a spectral method in the particular case of bimodal (symmetric\nand asymmetric) frequency distribution with or without external field. We also\nrecover in a very easy and intuitive way the only other known analytical\nresults: those corresponding to reflection-symmetric bimodal frequency\ndistributions near bifurcation points.",
"arxiv_id": "patt-sol/9706003",
"authors": [
"J. A. Acebron",
"L. L. Bonilla"
],
"categories": [
"patt-sol",
"adap-org",
"cond-mat.dis-nn",
"nlin.AO",
"nlin.PS"
],
"doi": "10.1016/S0167-2789(97)00197-8",
"title": "Asymptotic description of transients and synchronized states of globally coupled oscillators",
"url": "https://arxiv.org/abs/patt-sol/9706003"
},
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