论文标题
与随机干扰的耦合相振荡器的同步和图的周期空间
Synchronization of Coupled Phase Oscillators with Stochastic Disturbances and the Cycle Space of the Graph
论文作者
论文摘要
讨论了复杂的耦合相振荡器的复杂网络系统的同步稳定性。如果网络受到干扰的影响，则可以使用耦合相振荡器的随机线性化系统来确定节点之间线差的相位差异，并确定可能导致不同步的脆弱线。主要结果是相位差异的渐近方差矩阵的推导，该差异表征了波动的严重程度。发现系统图的循环空间在此表征中起作用。通过循环空间理论，评估形成小周期对波动的影响。事实证明，添加一条新线路或提高线路的耦合强度会影响任何周期中的线的波动，包括该线，而它不会影响其他线路的波动。特别是，如果这些动作没有改变同步状态的相位差异，则影响的波动减少。
The synchronization stability of a complex network system of coupled phase oscillators is discussed. In case the network is affected by disturbances, a stochastic linearized system of the coupled phase oscillators may be used to determine the fluctuations of phase differences in the lines between the nodes and to identify the vulnerable lines that may lead to desynchronization. The main result is the derivation of the asymptotic variance matrix of the phase differences which characterizes the severity of the fluctuations. It is found that the cycle space of the graph of the system plays a role in this characterization. With theory of the cycle space, the effect of forming small cycles on the fluctuations are evaluated. It is proven that adding a new line or increasing the coupling strength of a line affect the fluctuations in the lines in any cycle including this line while it does not affect the fluctuations in the other lines. In particular, if the phase differences at the synchronous state are not changed by these actions, then the affected fluctuations reduce.
