Classes of critical avalanche dynamics in complex networks

Abstract

Dynamical processes exhibiting absorbing states are essential in the modeling of a large variety of situations from material science to epidemiology and social sciences. Such processes exhibit the possibility of avalanching behavior upon slow driving. Here, we study the distribution of sizes and durations of avalanches for well-known dynamical processes on complex networks. We find that all analyzed models display a similar critical behavior, characterized by the presence of two distinct regimes. At small scales, sizes and durations of avalanches exhibit distributions that are dependent on the network topology and the model dynamics. At asymptotically large scales instead -- irrespective of the type of dynamics and of the topology of the underlying network -- sizes and durations of avalanches are characterized by power-law distributions with the exponents of the standard mean-field critical branching process.

arXiv comment10 pages, 4 figures, Supplemental Material available at this http://homes.sice.indiana.edu/filiradi/Mypapers/Avalanches/SM.pdf

References in corpus (36)

• Emergence of scaling in random networks
• Statistical physics of social dynamics
• Epidemic processes in complex networks
• Random graphs with arbitrary degree distributions and their applications
• Resilience of the Internet to random breakdowns
• Critical phenomena in complex networks
• Crackling Noise
• Generation of uncorrelated random scale-free networks
• Modeling Cascading Failures in the North American Power Grid
• Unified Scaling Law for Earthquakes
• Random walks and diffusion on networks
• Colloquium: Criticality and dynamical scaling in living systems
• Voter Models on Heterogeneous Networks
• Localization and Spreading of Diseases in Complex Networks
• Percolation Critical Exponents in Scale-Free Networks
• Percolation on sparse networks
• Self-Organized Branching Processes: A Mean-Field Theory for Avalanches
• The Spontaneous Emergence of Social Influence in Online Systems
• Sandpile on Scale-Free Networks
• Avalanche and spreading exponents in systems with absorbing states
• Structural and Dynamical Patterns on Online Social Networks: the Spanish May 15th Movement as a case study
• Scale-free Networks Well Done
• Competition-induced criticality in a model of meme popularity
• Langevin approach for the dynamics of the contact process on annealed scale-free networks
• Predicting percolation thresholds in networks
• Self-organized criticality in X-ray flares of gamma-ray burst afterglows
• Social Contagion: An Empirical Study of Information Spread on Digg and Twitter Follower Graphs
• Statistical Properties of Avalanches in Networks
• The average shape of a fluctuation: universality in excursions of stochastic processes
• Power Law Distributions of Offspring and Generation Numbers in Branching Models of Earthquake Triggering
• Breaking of the site-bond percolation universality in networks
• A simple unified view of branching process statistics: random walks in balanced logarithmic potentials
• Quasi-Neutral theory of epidemic outbreaks
• Description of spreading dynamics by microscopic network models and macroscopic branching processes can differ due to coalescence
• Analytical study of quality-biased competition dynamics for memes in social media
• Avalanches in an excitable network

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