小振荡同步
Synchronization of small oscillations
摘要：
研究了一组全同振子在小振动下的同步问题。整体耦合由一对矩阵加权拉普拉斯矩阵描述;一个代表耗散，另一个代表恢复连接器。提出了一种将这两个实矩阵合并为一个复矩阵的构造方法。结果表明，振子在稳态时是否同步取决于该复矩阵在虚轴上的特征值个数。这种情况下的特殊情况下，恢复性耦合是弱或不存在的某些改进，也提出。
英文摘要：
Synchronization is studied in an array of identical oscillators undergoing small vibrations. The overall coupling is described by a pair of matrix-weighted Laplacian matrices; one representing the dissipative, the other the restorative connectors. A construction is proposed to combine these two real matrices in a single complex matrix. It is shown that whether the oscillators synchronize in the steady state or not depends on the number of eigenvalues of this complex matrix on the imaginary axis. Certain refinements of this condition for the special cases, where the restorative coupling is either weak or absent, are also presented.
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