恢复耦合下谐振子的同步及其在电网络中的应用
Synchronization of harmonic oscillators under restorative coupling with applications in electrical networks
摘要：
研究了恢复耦合对耦合同谐振子同步的作用。给出了各个系统的解收敛于公共轨线的充要条件。通过简单的物理实例，阐述了定理的意义和局限性。此外，为了证明他们的多功能性，结果扩展到覆盖LTI无源电气网络。其中一个推广推广了同步子空间的渐近稳定性和拉普拉斯矩阵的第二小特征值之间的著名联系。
英文摘要：
The role of restorative coupling on synchronization of coupled identical harmonic oscillators is studied. Necessary and sufficient conditions, under which the individual systems' solutions converge to a common trajectory, are presented. Through simple physical examples, the meaning and limitations of the theorems are expounded. Also, to demonstrate their versatility, the results are extended to cover LTI passive electrical networks. One of the extensions generalizes the well-known link between the asymptotic stability of the synchronization subspace and the second smallest eigenvalue of the Laplacian matrix.
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