Critical phenomena in the dynamical visibility graph

TL;DR

This paper explores how the relative number of clusters in dynamic visibility graphs derived from various time series exhibits power law behavior near a critical angle, revealing phase transition-like phenomena.

Contribution

It introduces a novel approach linking time series analysis with phase transition theory through the study of dynamic visibility graphs.

Findings

Power law dependence of cluster number near critical angle

Similarity to second-order phase transition behavior

Each time series has a unique critical index

Abstract

We have investigated the time series by the mapping them to the complex network. We have studied the behavior of the relative number of clusters in dynamic visibility graphs near the critical value of the angle of view. Time series of different nature both artificial and experimental were numerically investigated. In all cases, the dependence of the relative number of clusters on the proximity to the critical angle of view had a power law behavior. Thus, it was shown that there is a similarity between the behavior of the relative number of clusters and the order parameter in the second-order phase transition theory and percolation theory. Each time series is characterized by its own value of the critical index - an analog of the critical index in second-order phase transition theory.