Burstiness and fractional diffusion on complex networks

  • Sarah de Nigris
  • Anthony Hastir
  • Renaud Lambiotte
Regular Article

DOI: 10.1140/epjb/e2016-60947-3

Cite this article as:
de Nigris, S., Hastir, A. & Lambiotte, R. Eur. Phys. J. B (2016) 89: 114. doi:10.1140/epjb/e2016-60947-3
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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.

Keywords

Statistical and Nonlinear Physics 

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Sarah de Nigris
    • 1
  • Anthony Hastir
    • 1
  • Renaud Lambiotte
    • 1
  1. 1.naXys, University of NamurNamurBelgium