Talk:Kuramoto model

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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)

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