Extreme events in a complex network: interplay between degree distribution and repulsive interaction

TL;DR

This paper investigates how topological heterogeneity and mean-field repulsive interactions in complex networks induce extreme events, revealing that node degree influences vulnerability at different interaction strengths and that these events are linked to boundary transitions in oscillator dynamics.

Contribution

It introduces a combined analysis of degree distribution and repulsive interactions as a mechanism for extreme events in complex networks, supported by a phase model and annealed network approximation.

Findings

High degree nodes are vulnerable to weaker repulsive interactions.

Low degree nodes are susceptible to stronger interactions.

Extreme events occur near the transition boundary from rotation to libration.

Abstract

The role of topological heterogeneity in the origin of extreme events in a network is investigated here. The dynamics of the oscillators associated with the nodes are assumed to be identical and influenced by mean-field repulsive interactions. An interplay of topological heterogeneity and the repulsive interaction between the dynamical units of the network triggers extreme events in the nodes when each node succumbs to such events for discretely different ranges of repulsive coupling. A high degree node is vulnerable to weaker repulsive interactions, while a low degree node is susceptible to stronger interactions. As a result, the formation of extreme events changes position with increasing strength of repulsive interaction from high to low degree nodes. Extreme events at any node are identified with the appearance of occasional large-amplitude events (amplitude of the temporal dynamics) that are larger than a threshold height and rare in occurrence, which we confirm by estimating the probability distribution of all events. Extreme events appear at any oscillator near the boundary of transition from rotation to libration at a critical value of the repulsive coupling strength. To explore the phenomenon, a paradigmatic second-order phase model is used to represent the dynamics of the oscillator associated with each node. We make an annealed network approximation to reduce our original model and thereby confirm the dual role of the repulsive interaction and the degree of a node in the origin of extreme events in any oscillator.