论文标题
谐波同步在所有三种类型的耦合下：位置，速度和加速度
Harmonic synchronization under all three types of coupling: position, velocity, and acceleration
论文作者
论文摘要
研究了通过位置，速度和加速耦合互连的相同谐波振荡器的同步。如何构建代表整体耦合的复杂拉普拉斯矩阵。结果表明，振荡器渐近同步并且仅当该矩阵在假想轴上具有单个特征值。该结果概括了一些已知的同步光谱测试。只要耦合图满足了某些结构条件，也证明了一些更简单的拉普拉斯构造可以工作。
Synchronization of identical harmonic oscillators interconnected via position, velocity, and acceleration couplings is studied. How to construct a complex Laplacian matrix representing the overall coupling is presented. It is shown that the oscillators asymptotically synchronize if and only if this matrix has a single eigenvalue on the imaginary axis. This result generalizes some of the known spectral tests for synchronization. Some simpler Laplacian constructions are also proved to work provided that certain structural conditions are satisfied by the coupling graphs.
