连续混沌系统时间序列的可视图分析  

Continuous chaotic time series analysis by means of visibility graph

作　　者：张蓉[1] 邹勇[1] 

机构地区：[1]华东师范大学物理系,上海200062

出　　处：《中国科技论文》2016年第5期554-556,565,共4页China Sciencepaper

基　　金：高等学校博士学科点专项科研基金资助项目(20130076120003)

摘　　要：以连续混沌系统时间序列为例,通过可视图方法分析其可行性,研究结果表明网络的度分布并不是幂率分布;并且发现同一个混沌系统的两个变量所对应的度序列之间存在很大的关联性,且序列中大数值点基本上都没有成为网络中的大度点。通过详细的对比分析得出时间序列的二阶导数和网络度大的节点间存在一定关系。可视图的全局统计量可以很好刻画系统的分岔过程,因此,可视图方法完全可以用来分析连续混沌系统的时间序列。By applying visibility graph analysis to time series produced by continuous chaotic systems,degree distributions of the resulted networks are shown to be non-power laws.Degree sequences of two variables have strong correlations.Furthermore,large sampled values of the series are not transformed into hubs in the networks.A detailed comparative analysis shows that there are some mild correlations between the degree sequence and the associated second derivative of underlying time series.The bifurcation process has been successfully captured by the global network statistical measures,which therefore suggests that visibility graphs can be used to analyze time series of continuous chaotic systems.

关 键 词：复杂网络 非线性时间序列 混沌 

分 类 号：O415.5[理学—理论物理] O157.5[理学—物理]