基于去趋势波动分析法的复杂网络同步研究

Synchronization Behavior of Complex Network using Detrended Fluctuation Analysis

应用去趋势波动分析(DFA)法研究了复杂网络的同步性。首先简要介绍DFA法,引入DFA标度指数,它能反映数据序列间的时空长范围相关性。然后应用DFA法研究Kuramoto网络模型的相同步和以随机激励下范德波振子为节点的复杂网络模型的完全同步。通过与其他同步性指标作对比,研究结果表明DFA标度指数作为同步性指标之一,可以很好地反映本文中的两种复杂网络模型的同步行为,与其他同步性指标一起可以研究其他复杂网络系统的同步性。

The approach of detrended fluctuation analysis （DFA） was taken to analyze synchronization of various complex networks. First, the DFA method was presented briefly, which permits the detection of long-range correlations in data series characterized by a scaling exponent. Then, this DFA method was a- dopted in the studies of network synchronization for two typical cases, i.e., the classic Kuramoto model, and the linearly and diffusively coupled networks with each node being a Van der Pol oscillator subject to parametric excitation. By comparing with other index parameters of network synchronization, it was found that the DFA scaling exponent can be applied to determine the synchronization behavior of these two complex networks. Moreover, the DFA scaling exponent can be further applied to study the synchroniza- tion of other complex networks.