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)

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)

References[edit]

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[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)

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)