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

## TL;DR

This paper investigates how non-Markovian recovery processes with memory influence failure propagation in complex networks, revealing that such memory effects can enhance network resilience against large-scale failures.

## Contribution

It introduces a pair approximation analysis considering non-Markovian recovery with delay, demonstrating that memory can unexpectedly improve network robustness.

## Key findings

- Non-Markovian recovery can reduce large-scale failure likelihood.
- Memory effects enhance network resilience in both natural and engineered systems.
- The analysis provides insights for designing more robust networks.

## 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.