Multiscale complex network for analyzing experimental multivariate time series

The multiscale phenomenon widely exists in nonlinear complex systems. One efficient way to characterize complex systems is to measure time series and then extract information from the measurements. We propose a reliable method for constructing a multiscale complex network from multivariate time series. In particular, for a given multivariate time series, we first perform a coarse-grained operation to define temporal scales and then reconstruct the multivariate phase-space for each scale to infer multiscale complex networks. In addition, we develop a novel clustering coefficient entropy to assess the derived multiscale complex networks, aiming to characterize the coupled dynamical characteristics underlying multivariate time series. We apply our proposed approach to the analysis of multivariate time series measured from gas-liquid two-phase flow experiments. The results yield novel insights into the inherent coupled flow behavior underlying a realistic multiphase flow system. Bridging multiscale analysis and complex network provides a fascinating methodology for probing multiscale complex behavior underlying complex systems.