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arXiv · 1602.00643

Burstiness and fractional diffusion on complex networks

Sarah De Nigris·Anthony Hastir·Renaud Lambiotte
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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.

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Sarah De Nigris, Anthony Hastir, Renaud Lambiotte. 2016-02-01. Burstiness and fractional diffusion on complex networks. https://doi.org/10.1140/epjb%2Fe2016-60947-3

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