Identification of Dynamical Behavior of Pseudoperiodic Time Series by Network Community Structure

Abstract

Although some transformation mappings demonstrate that different time series result in networks with distinct topological properties, it remains unclear whether the community structure in networks is related to the dynamical characteristics of the original time series. In this brief, we capture the underlying deterministic dynamics of a time series with intrinsic community structure of the corresponding network on the basis of a novel transformation method. Specifically, our findings suggest that there exist strong associations between the community structure in networks and the dynamical regimes of the time series. Emphasis is put on identifying typical characteristics of chaotic time series in terms of the variation trend of the community structure in the transformed network, especially taking the unstable periodic orbits of the dynamical system into consideration. Notably, the community structure characterizes the initial sensitivity and ergodicity of chaotic time series well. Moreover, sparse chaotic attractors and filled-in chaotic attractors are distinguished by the network community structure.