Eur. Phys. J. B (2016) 89: 114
https://doi.org/10.1140/epjb/e2016-60947-3

Regular Article

Burstiness and fractional diffusion on complex networks

naXys, University of Namur, Rempart de la Vierge 8, 5000 Namur, Belgium

^a e-mail: denigris.sarah@gmail.com

Received: 9 December 2015
Received in final form: 14 March 2016
Published online: 2 May 2016

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.