Correlations, fluctuations, and stability of a finite-size network of coupled oscillators
Correlations, fluctuations, and stability of a finite-size network of coupled oscillators
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DOI：
10.1103/physreve.76.031118
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发表时间：
2007-09-01
影响因子：
2.4
通讯作者：
Chow, Carson C.
中科院分区：
文献类型：
--
作者：
Buice, Michael A.;Chow, Carson C.
在平均场理论中，仓本耦合振子模型的非相干态具有边缘模。我们证明，由于有限尺寸效应的修正使这些模式在亚临界情况下稳定，即，当人口不同步时。这一演示是由一个非平衡统计场理论的耦合振子的一般模型制定的建设。这个理论与以前的结果是一致的。在所有对所有的情况下，这个理论中的波动完全是由于有限的尺寸修正，这可以在1/N的展开中计算，其中N是振子的数量。该理论的N ->无穷大极限就是传统上所谓的仓本模型的平均场理论。
The incoherent state of the Kuramoto model of coupled oscillators exhibits marginal modes in mean field theory. We demonstrate that corrections due to finite size effects render these modes stable in the subcritical case, i.e., when the population is not synchronous. This demonstration is facilitated by the construction of a nonequilibrium statistical field theoretic formulation of a generic model of coupled oscillators. This theory is consistent with previous results. In the all-to-all case, the fluctuations in this theory are due completely to finite size corrections, which can be calculated in an expansion in 1/N, where N is the number of oscillators. The N ->infinity limit of this theory is what is traditionally called mean field theory for the Kuramoto model.