基于矩的小世界振子网络同步分析
Moment-Based Analysis of Synchronization in Small-World Networks of Oscillators
摘要：
本文研究了耦合非线性振子小世界网络的同步问题。该网络通过在最近邻环中引入随机捷径来构造。同步状态的局部稳定性与网络拉普拉斯矩阵特征值分布的支持度密切相关。我们介绍，为第一次，解析表达式的拉普拉斯矩阵的特征值分布的前三个时刻的函数的概率的捷径和连接的基础最近邻耦合环。我们应用这些表达式来估计拉普拉斯矩阵的谱支撑，以预测小世界网络中的同步。我们验证了我们的预测与数值模拟的效率。
英文摘要：
In this paper, we investigate synchronization in a small-world network of coupled nonlinear oscillators. This network is constructed by introducing random shortcuts in a nearest-neighbors ring. The local stability of the synchronous state is closely related with the support of the eigenvalue distribution of the Laplacian matrix of the network. We introduce, for the first time, analytical expressions for the first three moments of the eigenvalue distribution of the Laplacian matrix as a function of the probability of shortcuts and the connectivity of the underlying nearest-neighbor coupled ring. We apply these expressions to estimate the spectral support of the Laplacian matrix in order to predict synchronization in small-world networks. We verify the efficiency of our predictions with numerical simulations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
