Random walks on networks with preferential cumulative damage: generation of bias and aging

In this paper, we explore the reduction of functionality in a complex system as consequence cumulative random damage and imperfect reparation, phenomenon modeled dynamical process on networks. We analyze global characteristics diffusive movement walkers networks where hop considering capacity transport each link. The links are susceptible to that generates bias aging. describe algorithm for generation producing eigenvalues transition matrix defines walker different types graphs, including regular, deterministic, evolution asymmetry is quantified with local information further non-local associated scale such mean first passage times fractional Laplacian matrix. Our findings suggest systems greater complexity live longer.