Permutation Entropy of State Transition Networks to Detect Synchronization

Abstract

The dynamic behavior of many physical, biological, and other systems, are organized according to the synchronization of chaotic oscillators. In this paper, we have proposed a new method with low sensitivity to noise for detecting synchronization by mapping time series to complex networks, called the ordinal partition network, and calculating the permutation entropy of that structure. We show that this method can detect different kinds of synchronization such as complete synchronization, phase synchronization, and generalized synchronization. In all cases, the estimated permutation entropy decreases with increased synchronization. This method is also capable of estimating the topology of the network graph from the time series, without knowledge of the dynamical equations of individual nodes. This approach has been applied for the two identical and nonidentical coupled Rössler systems, two nonidentical coupled Lorenz systems, and a ring of coupled Lorenz96 oscillators.

Unveiling the Connectivity of Complex Networks Using Ordinal Transition Methods

“…Ordinal methods offer good potential for various applications, particularly in finding correlations between time series. The multivariate extension of these methods enables the synthesis of information from multiple data sources, resulting in a unified set of symbols [24][25][26] . This approach proves useful in detecting phase transitions within the collective state of small groups of coupled chaotic nodes.…”

“…These examples highlight the significant potential of ordinal methods in studying dynamical ensembles and networks. However, it is important to note that most of these applications currently remain confined to proof-of-concept studies involving small networks [24,25]. In addition, many of these approaches rely on multivariate pairwise correlations to extract information [4].…”