相位振荡器网络完全同步的扰动分析
Perturbation Analysis of Complete Synchronization in Networks of Phase Oscillators
摘要：
弱耦合自持振子的行为通常可以用相位方程很好地描述。在这里，我们使用的范式仓本相位振荡器耦合在一个网络中计算一阶和二阶校正的频率完全同步状态的非全同振荡器。底层耦合网络的拓扑结构反映在以特定方式影响同步频率的网络拉普拉斯算子的特征值和特征向量中。它们描述了网络中节点的重要性以及它们之间的关系。对于一类无标度随机网络和Erdens-Rényi随机网络，得到了具有猝灭随机频率的振子的同步频率的期望值.本文简要讨论了二阶微扰理论在网络结构分析中的应用。
英文摘要：
The behavior of weakly coupled self-sustained oscillators can often be well described by phase equations. Here we use the paradigm of Kuramoto phase oscillators which are coupled in a network to calculate first and second order corrections to the frequency of the fully synchronized state for nonidentical oscillators. The topology of the underlying coupling network is reflected in the eigenvalues and eigenvectors of the network Laplacian which influence the synchronization frequency in a particular way. They characterize the importance of nodes in a network and the relations between them. Expected values for the synchronization frequency are obtained for oscillators with quenched random frequencies on a class of scale-free random networks and for a Erdős-Rényi random network. We briefly discuss an application of the perturbation theory in the second order to network structural analysis.
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