Consistency between functional and structural networks of coupled nonlinear oscillators

Abstract

In data-based reconstruction of complex networks, dynamical information can be measured and exploited to generate a functional network, but is it a true representation of the actual (structural) network? That is, when do the functional and structural networks match and is a perfect matching possible? To address these questions, we use coupled nonlinear oscillator networks and investigate the transition in the synchronization dynamics to identify the conditions under which the functional and structural networks are best matched. We find that, as the coupling strength is increased in the weak-coupling regime, the consistency between the two networks first increases and then decreases, reaching maximum in an optimal coupling regime. Moreover, by changing the network structure, we find that both the optimal regime and the maximum consistency will be affected. In particular, the consistency for heterogeneous networks is generally weaker than that for homogeneous networks. Based on the stability of the functional network, we propose further an efficient method to identify the optimal coupling regime in realistic situations where the detailed information about the network structure, such as the network size and the number of edges, is not available. Two real-world examples are given: corticocortical network of cat brain and the Nepal power grid. Our results provide new insights not only into the fundamental interplay between network structure and dynamics but also into the development of methodologies to reconstruct complex networks from data.

Consistency of heterogeneous synchronization patterns in complex weighted networks

“…This allows to construct robust functional networks that have reminiscent characteristics of the structural network for increasing values of the consistency thresholds imposed. Previous research shows that, in unweighted and undirected networks, for certain coupling regimes there is an optimal matching between structural and functional networks [12]. Here we extend these results to the case of weighted undirected networks.…”

“…In the past, studies of the synchronization patterns in networks of oscillators were mainly aimed at describing the conditions associated with the emergence of specific synchronization patterns in all the nodes [10]. In the particular case of complex networks of coupled nonlinear oscillators, recent studies have provided evidence that it * Electronic address: daniel.malagarriga@upc.edu; Corresponding author is possible to identify an appropriate interaction regime that allows to collect measured data to infer the underlying network structure based on time-series statistical similarity analysis [11] or connectivity stability analysis [12]. In real-life systems, such as ecological networks [13], brain oscillations [14][15][16][17] or climate interactions [18], various types of complex synchronized dynamics have been observed.…”

Model reconstruction from temporal data for coupled oscillator networks

“…Network reconstruction is an active area of research [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29]. In section 2.2, we review the literature most closely related to our approach.…”

Model-free inference of direct network interactions from nonlinear collective dynamics

“…Common model-free approaches not considering the nonlinear system dynamics construct functional links by detecting statistical dependencies (e.g., correlations, mutual information, Granger causality, and extensions thereof) [23][24][25][26][27][28][29][30][31] and thus are prone to recover indirect interactions among the units of a network, for instance, due to common external inputs or decorrelating effects induced by other units in the network 11,27,28,[32][33][34] . Although latest efforts have focused on filtering indirect connections 27,28 from pairwise statistical dependencies, recent studies show that these functional links can only match direct connections under specific homogeneity conditions 35 , which rarely occur in real-world systems.…”