基于动力学同步的复杂网络结构识别速度研究

Analysis the convergency speed of estimating the network topology based on the dynamical synchronization

基于动力学同步的复杂网络结构识别是探测复杂网络拓扑性质的重要方面,其中识别速度是一个重要但鲜有讨论问题.首先对弱耦合条件下耦合非线性振子网络结构识别速度的问题进行了研究.发现识别速度随耦合强度成正比增长.通过解析讨论,肯定了这一关系是普适的.之后基于我们最近提出的反复驱动识别方法,将处于同步稳定态的耦合区域也纳入研究范围.在这种情形下存在一个最佳的时间片段的长度使识别速度达到极值.这些结论加深了对时间序列中蕴含的拓扑结构信息量的理解.

Identifying convergent speed is an important but rarely discussed problem in estimating topologies of complex networks. In this paper, we discuss this problem mainly in both weakly and strongly coupled conditions. In the weakly coupled conditions, the convergent speed we defined increases linearly with coupling strength increasing. After analyzing the dynamics, we find that this relation is universal. In light of the repeatedly driving method we proposed recently, we generalize the definition of the convergent speed into the area of synchronization. In this case, there is a best length of the driving time series to maximize the convergent speed. The knowledge of convergent speed helps us understand the topological information embedded in the time series.