Non-Markovian recovery makes complex networks more resilient against large-scale failures

Zhao-Hua Lin,Chen Xu,Mi Feng,Zonghua Liu,Pak Ming Hui,Ming Tang,Ying-Cheng Lai

doi:10.1038/s41467-020-15860-2

Zhao-Hua Lin, Chen Xu + Show 5 more

Open Access

https://doi.org/10.1038/s41467-020-15860-2

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Abstract

Non-Markovian spontaneous recovery processes with a time delay (memory) are ubiquitous in the real world. How does the non-Markovian characteristic affect failure propagation in complex networks? We consider failures due to internal causes at the nodal level and external failures due to an adverse environment, and develop a pair approximation analysis taking into account the two-node correlation. In general, a high failure stationary state can arise, corresponding to large-scale failures that can significantly compromise the functioning of the network. We uncover a striking phenomenon: memory associated with nodal recovery can counter-intuitively make the network more resilient against large-scale failures. In natural systems, the intrinsic non-Markovian characteristic of nodal recovery may thus be one reason for their resilience. In engineering design, incorporating certain non-Markovian features into the network may be beneficial to equipping it with a strong resilient capability to resist catastrophic failures.

Highlights

Non-Markovian spontaneous recovery processes with a time delay are ubiquitous in the real world
Comparing results with numerical simulations indicates that both mean-field theory and pair approximation (PA) analysis capture the key features of the failure propagation dynamics qualitatively, but the PA analysis yields results that are in better quantitative agreement with numerics
In the non-Markovian recovery (NMR) model, an A-type node may fail spontaneously at the rate β1 to become an X-type node, or it may fail at the rate β2 to become a Y-type node when the number of its A-type neighboring nodes is less than or equal to a threshold integer value m that sets the limit on neighboring support for proper functioning of a node

Summary

Introduction

Non-Markovian spontaneous recovery processes with a time delay (memory) are ubiquitous in the real world. A node fails because of internal causes (e.g., the occurrence of some abnormal or undesired dynamical behaviors within the node), which is independent of the states of its neighbors In this case, the node can recover spontaneously after a period of time. A non-Markovian recovery (NMR) process has memory, as the current state of a node depends on the most recent state and on the previous states In this case, the interevent time distribution is not exponential but typically exhibits a heavy tail. We assume that the failed nodes due to internal and external causes will take different time to recover, so a memory effect is naturally built into the model. In engineering and infrastructure design, incorporating certain non-Markovian features into the network may help strengthen its resilience and robustness

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