The modeling and analysis of empirical systems with complex networks

Abstract

Network construction is an acceptable approach for better understanding the behavior of complex system which can be used to reveal the pattern of collective dynamics for realizing physical interactions in the dynamical system. In this case, characterizing functional connectivity of complex networks for studying a broad class of natural and artificial systems from the measures of correlation and causality is of utmost importance to correctly unravel physical phenomena of the system. Many network reconstruction approaches are based on heuristically thresholding the correlation matrices resulting from pairwise correlation analysis according to experimental methods. Other approaches compare the observed correlations against null models in the statistical analyses, obtaining results which are statistically more robust. Different methods were used, including cross-correlation (CC), spectral coherence (SpeCoh), mutual information (MI), transfer entropy (TE), Spearman's rank correlation (SC) and convergent cross-mapping (CCM). The methods were applied to linear and nonlinear collective dynamics by autoregressive moving average (ARMA) and Logistic map (LOG) models, respectively. The dynamics of interconnected units was simulated from different complex topologies widely observed in empirical systems with well-known network models. The methods of MI and CCM were chosen after examining on the artificial cases consisting of desirable features of the real-world systems.