Temporal profiles of avalanches on networks.


Journal Article

An avalanche or cascade occurs when one event causes one or more subsequent events, which in turn may cause further events in a chain reaction. Avalanching dynamics are studied in many disciplines, with a recent focus on average avalanche shapes, i.e., the temporal profiles of avalanches of fixed duration. At the critical point of the dynamics, the rescaled average avalanche shapes for different durations collapse onto a single universal curve. We apply Markov branching process theory to derive an equation governing the average avalanche shape for cascade dynamics on networks. Analysis of the equation at criticality demonstrates that nonsymmetric average avalanche shapes (as observed in some experiments) occur for certain combinations of dynamics and network topology. We give examples using numerical simulations of models for information spreading, neural dynamics, and behavior adoption and we propose simple experimental tests to quantify whether cascading systems are in the critical state.

Full Text

Duke Authors

Cited Authors

  • Gleeson, JP; Durrett, R

Published Date

  • October 31, 2017

Published In

Volume / Issue

  • 8 / 1

Start / End Page

  • 1227 -

PubMed ID

  • 29089481

Pubmed Central ID

  • 29089481

Electronic International Standard Serial Number (EISSN)

  • 2041-1723

International Standard Serial Number (ISSN)

  • 2041-1723

Digital Object Identifier (DOI)

  • 10.1038/s41467-017-01212-0


  • eng