期刊
TRANSPORT THEORY AND STATISTICAL PHYSICS
卷 34, 期 7, 页码 523-535出版社
TAYLOR & FRANCIS INC
DOI: 10.1080/00411450508951152
关键词
Kuvamoto model; mean field limit; coupled oscillators; kinetic theory
We discuss the application to systems of coupled nonlinear oscillators of methods originally developed for the Vlasov-Poisson equations of plasma kinetic theory. These methods lead to a simple but rigorous derivation of the infinite-oscillator limit for the well-known Kuramoto model, and also to a compact proof of global existence and uniqueness of solutions to the resulting Kuramoto-Sakaguchi equations. Vlasov-limit techniques can also be adapted to prove a central limit theorem for statistical ensembles of systems of oscillators. However, we emphasize that the noiseless Kuramoto model itself is strictly deterministic, and that the Kuramoto-Sakaguchi equations can be formulated without any reference to a stochastic distribution of oscillator frequencies.
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