Burstiness and fractional diffusion on complex networks

Sarah de Nigris (), Anthony Hastir and Renaud Lambiotte
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Sarah de Nigris: naXys, University of Namur
Anthony Hastir: naXys, University of Namur
Renaud Lambiotte: naXys, University of Namur

The European Physical Journal B: Condensed Matter and Complex Systems, 2016, vol. 89, issue 5, 1-7

Abstract: Abstract Many dynamical processes on real world networks display complex temporal patterns as, for instance, a fat-tailed distribution of inter-events times, leading to heterogeneous waiting times between events. In this work, we focus on distributions whose average inter-event time diverges, and study its impact on the dynamics of random walkers on networks. The process can naturally be described, in the long time limit, in terms of Riemann-Liouville fractional derivatives. We show that all the dynamical modes possess, in the asymptotic regime, the same power law relaxation, which implies that the dynamics does not exhibit time-scale separation between modes, and that no mode can be neglected versus another one, even for long times. Our results are then confirmed by numerical simulations.

Keywords: Statistical; and; Nonlinear; Physics (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1140/epjb/e2016-60947-3

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