# Talk:Kuramoto model

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## Untitled

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)

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

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

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)

#### References

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

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)

#### Partial Derivatives

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

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)

## WikiProject class rating

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)