Predicting Lifetime of Dynamical Networks Experiencing Persistent Random Attacks

TL;DR

This paper investigates how persistent random attacks influence the lifespan of dynamical networks, providing analytical and numerical insights into predicting critical failure points and network lifetime.

Contribution

It introduces a model for decaying networks under persistent attacks and derives analytical expressions for network lifetime based on attack magnitude and failure thresholds.

Findings

Network lifetime inversely related to attack magnitude

Logarithmic dependence of lifetime on failure threshold

Permanent attacks reduce network robustness

Abstract

Empirical estimation of critical points at which complex systems abruptly flip from one state to another is among the remaining challenges in network science. However, due to the stochastic nature of critical transitions it is widely believed that critical points are difficult to estimate, and it is even more difficult, if not impossible, to predict the time such transitions occur [1-4]. We analyze a class of decaying dynamical networks experiencing persistent attacks in which the magnitude of the attack is quantified by the probability of an internal failure, and there is some chance that an internal failure will be permanent. When the fraction of active neighbors declines to a critical threshold, cascading failures trigger a network breakdown. For this class of network we find both numerically and analytically that the time to the network breakdown, equivalent to the network lifetime, is inversely dependent upon the magnitude of the attack and logarithmically dependent on the threshold. We analyze how permanent attacks affect dynamical network robustness and use the network lifetime as a measure of dynamical network robustness offering new methodological insight into system dynamics.