  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.
