Characterization Of Nonlinear Time Series Based On Complex Networks

There is a common theme for science in 21th century, then the theme might be"exploring complexity". Chaos theory and complex network theory are the two main tools for the study of complexity. In this paper, we focus on the pseudoperiodic time series dynamic detection based on the complex networks. We mainly explore the statistical characterization of data in time domain and network topology and search the relationship between the dynamics of time series and the topological structure of networks. Pseudoperiodic data widely exist in nature. However, It is very difficult to detect the internal deterministic behavior hidden in the time series because of the presence of strong periodicity.First, we apply the method of cycle division to construct the network models of pseudoperiodic time series which possess different dynamics and then describe their topological structures with basic network statistics. Through the experiments, we find that both the network models of noisy periodic time series and chaotic data have small-world characteristics. However, the degree distributions of network in different threshold constructed from periodic data disturbed by the noise can be fitted by the Poisson distribution with different parameters. The chaotic data's network exhibit the multiple peaks in the degree distribution curve. As the threhold increases, the number of peak become more. In addition, we have descirbed the weighted networks and choose the vertex weight of every node as the statistics. We find that for noisy periodic time series, the vertex strength distribution exhibits a Gauss distribution. For the chaotic time series, it has a Power-Law distribution.Second, we research the relationship between the topology of complex network and dynamics of time series. In the paper, we apply the method of detecting power law distribution which bases upon the surrogate algorithm to analysis the weighted networks constructed from different chaotic data. We find that some data reject the zero hypothesis. Moreover, we generate several pseudoperiodic data which exhibit the small-world character and scale-free property. But these data have little chaotic dynamics. These results suggest that scale-free is not the inherent nature of chaotic data's network models.Finally, we detect the existence of underlying dynamics in normal vowels and search the longest time window that the vowel keeps its periodic dynamics. The human vowels have pseudoperiodic property which is possibly due to chaos. We employ a novel pseudoperiodic surrogate algorithm to detect the dynamics of chinese normal vowels. The results reveal that the measured chinese vowels are consistent with chaos. The longest time window is invariant for different vowel data and their timescale that keep periodic dynamics is between 25ms and 35ms. When the time length is long enough, it converts to chaotic dynamics.