【作者】 张蓉；

【导师】 邹勇；

【作者基本信息】 华东师范大学 ， 理论物理， 2016， 硕士

【摘要】 近来,可视图法为研究时间序列的动力学特性提供了复杂网络的思想和方法。可视图法是指把时间序列中的数据根据一定的规则映射为复杂网络中的节点,而两节点间是否连接取决于数据间的线性可视与否。随后,又有学者相继提出水平可视化算法和适用于消减分形序列中噪声影响的改进可视化算法。本文将选取不同的时间序列包括：连续混沌系统时间序列、分形时间序列和自回归时间序列,应用不同的可视图方法,分别构建可视图。通过构建后网络的度分布和网络统计量来研究网络的动力学特性,主要得到以下结论：1、连续混沌系统的两个函数关系独立的变量之间存在较大的度关联,网络全局统计量可以刻画系统的分岔和混沌过程。2、在自回归随机过程中,度分布用指数函数刻画。而在分数布朗运动中,度分布更合适用幂律函数刻画。这一结论不但适用于VG方法,同时也适用于HVG方法。3、修正后可视化算法的优点：保留了自回归时间序列的动力学特性；不同参数情况下的时间序列转化成网络后,率参数的收敛值都基本一致。4、在HVG算法下,自回归时间序列把网络度分布(呈指数分布)的率参数λ=ln(3/2)不能作为区分随机和混沌序列的临界值。本文的工作加深人们对于可视图法的理解和重要性的认识,并且对于进一步借助可视图法研究其他时间序列具有指导性意义和崭新的认识。更多还原

【Abstract】 Recently, visibility graph has provided much insight of the dynamics of time series from complex network perspectives. This algorithm is introduced as a mapping between time series and complex networks, while the connection of two nodes is determined by a linear visibility condition. Later, horizontal visibility graph and improved visibility graph have been proposed, which estimates fractality of time series reliably when noise is present.This article investigates various time series, including continuous chaotic systems, fractal and auto-regressive stochastic processes. By applying visibility graph analysis to these processes, degree distributions and global network measures capture some structure of time series. The main conclusions are the following:1. There are significant correlations between two independent variables of the same continuous chaotic system. The bifurcation routes to chaos have been successfully captured by global network measures.2. Degree distributions of the resulted complex networks of auto-regressive processes are characterized by exponential forms, while that of fractional Brownian motions fulfill power-law forms.3. The improved visibility graph preserves some structures of the auto-regressive processes. The visibility graph based on time series with different parameters shows the same convergence to exponential degree distributions.4. The critical exponent of degree distribution of horizontal visibility graph λ= ln(3/2) cannot distinguish randomness from chaos in time series.This article provides a better understanding of visibility graph. This approach can be applied to characterizing other time series from a new point of view.更多还原