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. This dynamics depends 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 controllability in
spatially embedded and random networks where spontaneous recovery of
components can mitigate spontaneous failure and damage spread in
dynamical networks.
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