Liapunov functionals and large-time-asymptotics of mean-field nonlinear Fokker-Planck equations

Anton Arnold; Luis L. Bonilla; Peter A. Markowich

doi:10.1080/00411459608203544

Liapunov functionals and large-time-asymptotics of mean-field nonlinear Fokker-Planck equations

Anton Arnold^*, Luis L. Bonilla, Peter A. Markowich

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

Large-time asymptotics of the solutions of time-dependent mean-field nonlinear Fokker-Planck systems are analyzed by exploiting the properties of Liapunov functionals (relative entropies). We first discuss the scalar Desai-Zwanzig model and then generalize the techniques to a general class of mean-field oscillator equations. Systems of this type are relevant in the modeling of synchronization of a large population of coupled nonlinear oscillators in the presence of external or thermal white noise.

Original language	English (US)
Pages (from-to)	733-751
Number of pages	19
Journal	Transport Theory and Statistical Physics
Volume	25
Issue number	7
DOIs	https://doi.org/10.1080/00411459608203544
State	Published - 1996
Externally published	Yes

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
Transportation
General Physics and Astronomy
Applied Mathematics

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10.1080/00411459608203544

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title = "Liapunov functionals and large-time-asymptotics of mean-field nonlinear Fokker-Planck equations",

abstract = "Large-time asymptotics of the solutions of time-dependent mean-field nonlinear Fokker-Planck systems are analyzed by exploiting the properties of Liapunov functionals (relative entropies). We first discuss the scalar Desai-Zwanzig model and then generalize the techniques to a general class of mean-field oscillator equations. Systems of this type are relevant in the modeling of synchronization of a large population of coupled nonlinear oscillators in the presence of external or thermal white noise.",

author = "Anton Arnold and Bonilla, {Luis L.} and Markowich, {Peter A.}",

year = "1996",

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T1 - Liapunov functionals and large-time-asymptotics of mean-field nonlinear Fokker-Planck equations

AU - Arnold, Anton

AU - Bonilla, Luis L.

AU - Markowich, Peter A.

PY - 1996

Y1 - 1996

N2 - Large-time asymptotics of the solutions of time-dependent mean-field nonlinear Fokker-Planck systems are analyzed by exploiting the properties of Liapunov functionals (relative entropies). We first discuss the scalar Desai-Zwanzig model and then generalize the techniques to a general class of mean-field oscillator equations. Systems of this type are relevant in the modeling of synchronization of a large population of coupled nonlinear oscillators in the presence of external or thermal white noise.

AB - Large-time asymptotics of the solutions of time-dependent mean-field nonlinear Fokker-Planck systems are analyzed by exploiting the properties of Liapunov functionals (relative entropies). We first discuss the scalar Desai-Zwanzig model and then generalize the techniques to a general class of mean-field oscillator equations. Systems of this type are relevant in the modeling of synchronization of a large population of coupled nonlinear oscillators in the presence of external or thermal white noise.

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U2 - 10.1080/00411459608203544

DO - 10.1080/00411459608203544

M3 - Article

AN - SCOPUS:0030376634

SN - 0041-1450

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EP - 751

JO - Transport Theory and Statistical Physics

JF - Transport Theory and Statistical Physics

IS - 7

ER -

Liapunov functionals and large-time-asymptotics of mean-field nonlinear Fokker-Planck equations

Abstract

ASJC Scopus subject areas

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