论文标题
同步和最佳网络结构的噪声稳定性
Noise stability of synchronization and optimal network structures
论文作者
论文摘要
我们提供了一个理论框架，用于量化嘈杂振荡器网络中的预期同步水平。通过围绕同步状态的线性化，我们使用标准技术使用一种标准技术来得出以下数量，作为网络laplacian的特征值和本征函数的功能，用于处理多变量的Ornstein-uhlenbeck流程：$ nydy $ a $ a $ a的差异的幅度：同步。通过这种方法，我们可以量化单个节点和链接对同步的影响。因此，可以利用我们的理论找到最佳的网络结构来实现最佳的同步。此外，当振荡器的噪声水平是异质的时，我们还可以找到最佳的振荡器配置，即，根据其噪声水平，将振荡器放置在给定网络中。我们将理论应用于多个示例网络，以阐明最佳网络结构和振荡器配置。
We provide a theoretical framework for quantifying the expected level of synchronization in a network of noisy oscillators. Through linearization around the synchronized state, we derive the following quantities as functions of the eigenvalues and eigenfunctions of the network Laplacian using a standard technique for dealing with multivariate Ornstein-Uhlenbeck processes: the magnitude of the fluctuations around a synchronized state and the disturbance coefficients $α_i$ that represent how strongly node $i$ disturbs the synchronization. With this approach, we can quantify the effect of individual nodes and links on synchronization. Our theory can thus be utilized to find the optimal network structure for accomplishing the best synchronization. Furthermore, when the noise levels of the oscillators are heterogeneous, we can also find optimal oscillator configurations, i.e., where to place oscillators in a given network depending on their noise levels. We apply our theory to several example networks to elucidate optimal network structures and oscillator configurations.
