Evidence of self-organized criticality in time series by the horizontal visibility graph approach

Abstract

Determination of self-organized criticality (SOC) is crucial in evaluating the dynamical behavior of a time series. Here, we apply the complex network approach to assess the SOC characteristics in synthesis and real-world data sets. For this purpose, we employ the horizontal visibility graph (HVG) method and construct the relevant networks for two numerical avalanche-based samples (i.e., sand-pile models), several financial markets, and a solar nano-flare emission model. These series are shown to have long-temporal correlations via the detrended fluctuation analysis. We compute the degree distribution, maximum eigenvalue, and average clustering coefficient of the constructed HVGs and compare them with the values obtained for random and chaotic processes. The results manifest a perceptible deviation between these parameters in random and SOC time series. We conclude that the mentioned HVG’s features can distinguish between SOC and random systems.

Hierarchical deposition and scale-free networks: A visibility algorithm approach

“…The essence of the VA is to create a network from a set of data by assigning a node to each datum and assigning edges based on the mutual visibility between two data, i.e., if a line of visibility is not "intersected" by any intermediate data. This algorithm was originally developed [28] to uncover structures in time series data, uch as finding signatures of self-organised criticality (SOC) in avalanche-based data [29], and it has found applications in astrophysics [30], medicine [31], fluid mechanics [32] and several other fields [33]. Generally, the VA comes in two types: the Natural Visibility Algorithm (NVA) and the Horizontal Visibility Algorithm (HVA).…”