Burstiness and fractional diffusion on complex networks
arXiv:1602.00643 · doi:10.1140/epjb/e2016-60947-3
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.
7 pages, 4 figures
References in corpus (10)
- Small But Slow World: How Network Topology and Burstiness Slow Down Spreading
- A Poissonian explanation for heavy-tails in e-mail communication
- Random Walks, Markov Processes and the Multiscale Modular Organization of Complex Networks
- Information dynamics shape the networks of Internet-mediated prostitution
- Temporal Heterogeneities Increase the Prevalence of Epidemics on Evolving Networks
- Spreading Dynamics Following Bursty Human Activity Patterns
- Fractional dynamics on networks: Emergence of anomalous diffusion and Lévy flights
- Steady state and mean recurrence time for random walks on stochastic temporal networks
- Spreading dynamics on networks: the role of burstiness, topology and non-stationarity
- Solvable non-Markovian dynamic network