Temporal profiles of avalanches on networks
arXiv:1612.06477 · doi:10.1038/s41467-017-01212-0
Abstract
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 that characterize the growth and decay of avalanches of fixed duration. At the critical point of the dynamics the average avalanche shapes for different durations can be rescaled so that they collapse onto a single universal curve. We apply Markov branching process theory to derive a simple 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; specifically, on networks with heavy-tailed degree distributions. We give examples using numerical simulations of models for information spreading, neural dynamics, and behaviour adoption and we propose simple experimental tests to quantify whether cascading systems are in the critical state.
Simulation codes and network data are available from http://www.ul.ie/gleesonj/avalanches
References in corpus (8)
- Epidemic processes in complex networks
- The structure and dynamics of multilayer networks
- Small But Slow World: How Network Topology and Burstiness Slow Down Spreading
- Can Cascades be Predicted?
- Sandpile on Scale-Free Networks
- Exactly solvable model of avalanches dynamics for Barkhausen crackling noise
- Dynamical Systems on Networks: A Tutorial
- Breaking of the site-bond percolation universality in networks
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