Frequency synchronization in random oscillator network

We study the frequency-synchronization of randomly coupled oscillators. By analyzing the continuum limit, we obtain the sufficient condition for the mean-field type synchronization. We especially find that the critical coupling constant $K$ becomes 0 in the random scale free network, $P(k)\propto k^{-\gamma}$, if $2 < \gamma \le 3$. Numerical simulations in finite networks are consistent with these analysis.