Assessment of visibility graph similarity as a synchronization measure for chaotic, noisy and stochastic time series

Abstract

Finding synchronization between the outputs of a dynamic system, which are represented mostly as time series, helps to characterize the system activities during an occurrence. An important issue in analyzing time series is that they may behave chaotically or stochastically. Therefore, applying a reliable synchronization measure which can capture the dynamic features of the system helps to quantify the interdependencies between time series, correctly. In this paper, we employ similarity measures based on visibility graph (VG) algorithms as an alternative and radically different way to measure the synchronization between time series. We assess the performance of VG-based similarity measures on chaotic, noisy and stochastic time series. In our experiments, we use the Rössler system and the noisy Hénon map as representative instances of chaotic systems, and the Kuramoto model for studying detection of synchronization between stochastic time series. Our study suggests that the similarity measure based on the horizontal VG algorithm should be favored to other measures for detecting synchronization between chaotic and stochastic time series.