Dynamic interdependence and competition in multilayer networks

Abstract

From critical infrastructure, to physiology and the human brain, complex systems rarely occur in isolation. Instead, the functioning of nodes in one system often promotes or suppresses the functioning of nodes in another. Despite advances in structural interdependence, modeling interdependence and other interactions between dynamic systems has proven elusive. Here we define a broadly applicable dynamic dependency link and develop a general framework for interdependent and competitive interactions between general dynamic systems. We apply our framework to studying interdependent and competitive synchronization in multi-layer oscillator networks and cooperative/competitive contagions in an epidemic model. Using a mean-field theory which we verify numerically, we find explosive transitions and rich behavior which is absent in percolation models including hysteresis, multi-stability and chaos. The framework presented here provides a powerful new way to model and understand many of the interacting complex systems which surround us. * Electronic address: michael.danziger@biu.ac.il † Electronic address: ivan.bms.2011@gmail.com but without a general framework or ability to uncover universal patterns between systems [26-28].arXiv:1705.00241v1 [cond-mat.stat-mech]

Explosive transitions induced by interdependent contagion-consensus dynamics in multiplex networks

“…These explosive transitions are very relevant due to the drastic changes induced by perturbations in the bi-stability regions. This finding adds to recent studies devoted to determine the conditions which lead to explosive phenomena in monolayer networks [41][42][43][44][45] as well as in multilayer networks [28,46,47].…”

Generalized k-core percolation on correlated and uncorrelated multiplex networks

“…Multiplexity, however, has shaken the network percolation theory and gained increasing relevance in the past few years as real-life complex systems are rarely found to be a single network but often an interdependent multilayer structure, where dysfunction of nodes in one layer can lead to failure of dependent nodes in other layers [13][14][15]. As a result, percolation properties of multiplex networks are drastically different from those of single networks.…”

Spreading of localized attacks on spatial multiplex networks with a community structure

“…This interdependence can cause a spread of damages, and lead to a cascade of failures and even entire system collapse. Therefore, many studies have been carried out to analyze cascading failures in interdependent networks [1][2][3][4][5][6][7][8][9][10][11]. Many of these studies have focused on the multiplex network model, which is an important example of an interdependent network where the same nodes are linked by different layers [12][13][14][15].…”