Burstiness and fractional diffusion on complex networks

Sarah De Nigris, Anthony Hastir, Renaud Lambiotte

Research output: Contribution to journalArticlepeer-review

Abstract

Many dynamical processes on real world networks display complex temporal patterns as, forinstance, a fat-tailed distribution of inter-events times, leading to heterogeneouswaiting times between events. In this work, we focus on distributions whose averageinter-event time diverges, and study its impact on the dynamics of random walkers onnetworks. The process can naturally be described, in the long time limit, in terms ofRiemann-Liouville fractional derivatives. We show that all the dynamical modes possess, inthe asymptotic regime, the same power law relaxation, which implies that the dynamics doesnot exhibit time-scale separation between modes, and that no mode can be neglected versusanother one, even for long times. Our results are then confirmed by numericalsimulations.

Original languageEnglish
Article number114
JournalEuropean Physical Journal B
Volume89
Issue number5
DOIs
Publication statusPublished - 1 May 2016

Keywords

  • Statistical and Nonlinear Physics

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