Talk:Kuramoto model

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Untitled[edit]

I'd like to add discussions of the following:

stability of various equilibria
variations on the model
unresolved questions about the model
applications of the model

I'd also like to make graphs or possibly videos showing:

the various solutions, for the same system with different K
the bifurcation diagram as K various

There should also be some references.

Dannya222 05:52, 30 October 2005 (UTC)[reply]

Nice, put it on. You can find something i have been working on in this .pdf https://sourceforge.net/p/iftthesiscultur/code/ci/master/tree/qualify/q_lckm_v3.pdf . Right now i cant organize properly for wikipedia, but i will when the midterm exams are finished

Stochastic Variation[edit]

This stochastic variation is also soluble:

Where the equilibrium state is described by energy function

$H\left({\boldsymbol {\phi }}\right)=-{\frac {J}{N}}\sum _{i<j}^{N}\cos \left(\phi _{j}-\phi _{i}+\alpha \right)$

Free energy in the thermodynamic limit

$f_{\infty }=-\lim _{N\to \infty }{\frac {1}{\beta N}}\log \int d{\boldsymbol {\phi }}\;e^{-\beta H\left({\boldsymbol {\phi }}\right)}$

may be written

$f_{\infty }=-{\frac {1}{\beta }}\log 2\pi +{\frac {1}{\beta }}\min _{q}\left\{{\frac {1}{2}}\beta J\left({\frac {\sin {\alpha }}{\alpha }}\right)q^{2}-\log I_{0}\left(\beta J\left({\frac {\sin {\alpha }}{\alpha }}\right)q\right)\right\}$

Other variables of interest follow as corollaries.

Obviously I could be more explicit if I were to add this to the main article...

Ali, July 2006

Hi Ali, what is this thermodynamics about ? there is no conservative hamiltonian in this system, nor there is any thermodynamical equations that holds true. Am i wrong ? or these equations are just extrapolation without any prior rigorous basis ? — Preceding unsigned comment added by 187.39.189.83 (talk) 08:10, 26 June 2013 (UTC)[reply]

References[edit]

Does anyone have a reference to Kuramoto's paper? That should be included. --M0nstr42 14:41, 19 October 2006 (UTC)[reply]

I have just inserted the relevant references (Kuramoto's first paper and his book). Ref: Strogatz, Physica D (2000).

The Reference to Cumin et al. seems a bit off-topic here (too special), unless it is explained in the article. Erik17 (talk) 14:27, 7 January 2013 (UTC)[reply]

Partial Derivatives[edit]

Hi, there is no reason for partial derivatives in kuramoto equations, since they are EDO, if there are any space dependence, it must be made explicit, otherwise it is a EDO and is not to be confused by the continuum limit. I changed that, thank you

Variations on the Models[edit]

Hi all, i settled the v0 of this part of the article, giving a small hint of the structure and the possible contents. Obvious a lot must be made and nothing there is permanent, iam expecting revisions, thank you. — Preceding unsigned comment added by 187.39.189.83 (talk) 22:05, 26 June 2013 (UTC)[reply]

Who is Daido[edit]

Hi, does anyone know who is Daido in "Kuramoto-Daido model"? I think is Hiroaki Daido, but I'm not sure. Lining Huo (talk) 15:19, 11 August 2022 (UTC)[reply]

WikiProject class rating[edit]

This article was automatically assessed because at least one WikiProject had rated the article as start, and the rating on other projects was brought up to start class. BetacommandBot 09:57, 10 November 2007 (UTC)[reply]