Burstiness and fractional diffusion on complex networks

Overview & Synopsis

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 timescale 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.