Synchronization frequency of the Kuramoto model for coupling matrix with constant rows The non-mean field version of the Kuramoto model is given by
$\dot \theta_i = \omega_i + \sum_j K_{ij} \sin(\theta_j-\theta_i)$
and its study is of considerable interest for understanding the synchronization of chaotic systems ($K_{ij}$ is called the coupling matrix). 
I am interested in a special case* of the form $\omega_i \equiv c_i \omega_0$, $K_{ij} \equiv c_i K_0$, viz.
$\dot \theta_i = c_i \left[ \omega_0 + K_0 \sum_j \sin(\theta_j-\theta_i) \right]$

Has this case been treated in the
  literature for $c_i$ specified in
  advance or sampled from some
  distribution? References dealing with
  this case would be very helpful. I am ignorant of the literature but have not been able to find anything after looking.

Perhaps this is better suited to physics.stackexchange, but in principle it seems like more of a mathematics problem to me.
[*Specifically, I have reason to think that a system of this or similar form, in which the individual components are identical up to their individual rates, would (for suitably large $K_0$) drive its components to a common frequency that is (at least related to) the arithmetic mean of the $\omega_i$. Results speaking to the synchronization frequency are therefore particularly interesting to me.]
 A: As far as literature goes:
"From Kuramoto to Crawford..." - S Strogatz: 
http://omnis.if.ufrj.br/~monica/ACMSM2008/StrogatzPD2000.pdf
"Synchronization in Complex Networks" - Arenas et al
http://arxiv.org/PS_cache/arxiv/pdf/0805/0805.2976v3.pdf
However,
The special case you mention can be reduced to the mean field kuramoto model by introducing 
a complex order parameter. 
$
re^{i \Psi} = \frac{1}{n}\sum\limits_{j=1}^n e^{i\theta_j}
$
So
$\dot\theta_i = \omega_i + K_ir\sin(\Psi - \theta_i)$
Also, if you let $\omega_i \rightarrow \Omega + \Delta\omega_i$  and $\theta_i \rightarrow  \theta_i + \Omega t $ where $\Omega$ is your mean frequency
you get
$\dot\theta_i = \Delta\omega_i + K_ir\sin(\Psi - \theta_i)$
with the mean of all $\Delta\omega_i$ are zero and most importantly, $\dot\theta_i = 0$ 
now corresponds to that oscillator running at your mean frequency.
Now if $K_i >\frac{2}{\pi g(0)} \forall i$ with $g$ the p.d.f for your $\Delta\omega_i$'s, then you'll definately get a large proportion of
oscillators synching to your mean frequency. (Strogatz' paper covers this derivation for constant $K$)
How many is a tough question, depending on your p.d.f.
For general $K_i$ i think Arenas' paper should provide a starting point. 
