Node-Level Resilience Loss in Dynamic Complex Networks

TL;DR

This paper introduces a sequential mean-field method to estimate node-level resilience in large complex networks with high accuracy, linking local dynamics to network topology and aiding risk assessment.

Contribution

It develops a novel, efficient approach to assess individual node resilience in large non-linear networks, enhancing understanding of resilience loss mechanisms.

Findings

Achieves up to 98% accuracy in resilience estimation after 1-3 steps

Identifies nodes at greatest risk of failure in ecological and biological networks

Provides a framework for predicting impact of perturbations and informing system design

Abstract

In an increasingly connected world, the resilience of networked dynamical systems is important in the fields of ecology, economics, critical infrastructures, and organizational behaviour. Whilst we understand small-scale resilience well, our understanding of large-scale networked resilience is limited. Recent research in predicting the effective network-level resilience pattern has advanced our understanding of the coupling relationship between topology and dynamics. However, a method to estimate the resilience of an individual node within an arbitrarily large complex network governed by non-linear dynamics is still lacking. Here, we develop a sequential mean-field approach and show that after 1-3 steps of estimation, the node-level resilience function can be represented with up to 98\% accuracy. This new understanding compresses the higher dimensional relationship into a one-dimensional dynamic for tractable understanding, mapping the relationship between local dynamics and the statistical properties of network topology. By applying this framework to case studies in ecology and biology, we are able to not only understand the general resilience pattern of the network, but also identify the nodes at the greatest risk of failure and predict the impact of perturbations. These findings not only shed new light on the causes of resilience loss from cascade effects in networked systems, but the identification capability could also be used to prioritize protection, quantify risk, and inform the design of new system architectures.