Impact of embedding on predictability of failure-recovery dynamics in networks

TL;DR

This paper investigates how embedding affects the predictability of failure and recovery dynamics in networks, revealing hysteresis and switching phenomena influenced by spatial structure and developing a unifying theoretical framework.

Contribution

It introduces a model combining internal failure, external failure, and recovery, and links its dynamics to contact processes, highlighting the role of spatial embedding in network stability.

Findings

Hysteresis and switching occur in a narrow parameter region for Euclidean lattices.

Embedding influences the loss of predictability in failure-recovery dynamics.

A unifying theory connects the model to contact processes, aiding understanding of spatially embedded networks.

Abstract

Failure, damage spread and recovery crucially underlie many spatially embedded networked systems ranging from transportation structures to the human body. Here we study the interplay between spontaneous damage, induced failure and recovery in both embedded and non-embedded networks. In our model the network's components follow three realistic processes that capture these features: (i) spontaneous failure of a component independent of the neighborhood (internal failure), (ii) failure induced by failed neighboring nodes (external failure) and (iii) spontaneous recovery of a component.We identify a metastable domain in the global network phase diagram spanned by the model's control parameters where dramatic hysteresis effects and random switching between two coexisting states are observed. The loss of predictability due to these effects depend on the characteristic link length of the embedded system. For the Euclidean lattice in particular, hysteresis and switching only occur in an extremely narrow region of the parameter space compared to random networks. We develop a unifying theory which links the dynamics of our model to contact processes. Our unifying framework may help to better understand predictability and controllability in spatially embedded and random networks where spontaneous recovery of components can mitigate spontaneous failure and damage spread in the global network.