Talk:Kuramoto model

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Comments:

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)

[edit] 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<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


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

[edit] 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)