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.
Highlights
In recent decades, various local and global techniques, operating in time, frequency, or wavelet domain, have been introduced for measuring synchronization among time series
We present the main results of our experimental study aimed at assessing the capability of the VGbased similarity techniques in measuring synchronization between chaotic, noisy and stochastic time series
We call these schemes as the SS-visibility graph (VG) and the SSHVG, where SS refers to state-space mapping
Summary
Various local and global techniques, operating in time, frequency, or wavelet domain, have been introduced for measuring synchronization among time series. The crosscorrelation function and its counterpart in the frequency domain, i.e., the coherence function, were the first linear methods developed for quantifying synchronization between time series (Barlow and Brazier 1954; Brazier 1968). These were followed by the development of nonlinear techniques based on mutual information (Panzeri et al 1999), nonlinear regression (da Silva et al 1989), and phase synchronization (Rosenblum et al 2004) among others, summarized. A new approach, like VG algorithm, that deal with the intrinsic nonlinearity by being intrinsically nonlinear are welcome, but
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