Random walks on networks with preferential cumulative damage: Generation of bias and aging
Résumé
In this paper, we explore the reduction of functionality in a complex
system as a consequence of cumulative random damage and imperfect reparation, a
phenomenon modeled as a dynamical process on networks. We analyze the global
characteristics of the diffusive movement of random walkers on networks that hop
considering the capacity of transport of each link, those links are susceptible to
damage that generates bias and aging. We describe the algorithm for the generation of
damage and the bias in the transport producing complex eigenvalues of the transition
matrix that defines the random walker for different types of graphs, including regular,
deterministic, and random networks. The evolution of the asymmetry of the transport
is quantified with local quantities that consider the information in the links and non-
local quantities associated with the transport on a global scale. Finally, we characterize
aging by the finding that systems with greater complexity live longer.
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