摘要翻译：
研究了通过随机网络耦合的随机频率振荡器系统的同步起始问题。利用平均场近似，我们刻画了有限尺寸网络的样本间涨落，并在临界区域内导出了相应的标度性质。对于度分布为$p(k)\sim k^{-\gamma}$的无标度网络，我们发现当$\gamma>5$时，有限尺寸指数$\bar{\nu}$取5/2的值，与全局耦合的Kuramoto模型相同。对于高度异构的网络($3<\gamma<5$)，$\bar{\nu}$和序参数指数$\beta$依赖于$\gamma$。由平均场理论得到的这些指数的解析表达式与大量数值模拟的数据非常吻合。
---
英文标题：
《Finite-size scaling of synchronized oscillation on complex networks》
---
作者：
Hyunsuk Hong, Hyunggyu Park, and Lei-Han Tang
---
最新提交年份：
2007
---
分类信息：

一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
--

---
英文摘要：
  The onset of synchronization in a system of random frequency oscillators coupled through a random network is investigated. Using a mean-field approximation, we characterize sample-to-sample fluctuations for networks of finite size, and derive the corresponding scaling properties in the critical region. For scale-free networks with the degree distribution $P(k)\sim k^{-\gamma}$ at large $k$, we found that the finite size exponent $\bar{\nu}$ takes on the value 5/2 when $\gamma>5$, the same as in the globally coupled Kuramoto model. For highly heterogeneous networks ($3<\gamma <5$), $\bar{\nu}$ and the order parameter exponent $\beta$ depend on $\gamma$. The analytic expressions for these exponents obtained from the mean field theory are shown to be in excellent agreement with data from extensive numerical simulations.
---
PDF链接：
https://arxiv.org/pdf/710.1137