title: Analytical solution and scaling of fluctuations in complex networks traversed by damped, interacting random walkers.
abstract: A general model for random walks (RWs) on networks is proposed. It incorporates damping and time-dependent links, and it includes standard (undamped, noninteracting) RWs (SRWs), coalescing RWs, and coalescing-branching RWs as special cases. The exact, time-dependent solutions for the average numbers of visits (w) to nodes and their fluctuations (σ2) are given, and the long-term σ-w relation is studied. Although σ ∝ w(1/2) for SRWs, this power law can be fragile when coalescing-branching interaction is present. Damping, however, often strengthens it but with an exponent generally different from 1/2.
authors.affiliation: National Center for Biotechnology Information, National Library of Medicine, National Institutes of Health, 8600 Rockville Pike, Bethesda, Maryland 20894, USA.
authors.forename: Mehdi Bagheri
authors.initials: MB
authors.lastname: Hamaneh
authors.affiliation: National Center for Biotechnology Information, National Library of Medicine, National Institutes of Health, 8600 Rockville Pike, Bethesda, Maryland 20894, USA.
authors.forename: Jonah
authors.initials: J
authors.lastname: Haber
authors.affiliation: National Center for Biotechnology Information, National Library of Medicine, National Institutes of Health, 8600 Rockville Pike, Bethesda, Maryland 20894, USA.
authors.forename: Yi-Kuo
authors.initials: YK
authors.lastname: Yu
mesh_terms: D008962:Models, Theoretical; D013269:Stochastic Processes