Abstract
This paper studies statistical properties of avalanche dynamical models on complex network topologies. The authors provide numerical and theoretical evidence of a universal critical behavior. Both the size and the duration of avalanches obey power-law distributions characterized by two distinct scaling regimes: at small scales, the statistics of the avalanches is model and network dependent; at large scale instead, the distribution of the avalanche sizes and durations is identical for all networks and types of dynamics.
Highlights
In this paper, we study seven stochastic models that are prototypical to describe the diffusion of some sort of “activity” in networks [1,2]
We found that any minimal deviation from the assumptions underlying the mapping into an anomalous branching process brings the system back to the realm of standard MF and its associated superuniversal exponents, so that anomalous exponents are exceedingly difficult to observe
Our results suggest this statement to be true for seven wellknown avalanche dynamical models, but we believe that it can be extended to many other spreading processes taking place on networks
Summary
We study seven stochastic models that are prototypical to describe the diffusion of some sort of “activity” in networks [1,2]. Equation (2) defines the so-called “standard” mean-field (MF) or “branching process” exponents This type of scaling is expected to emerge for critical avalanches in the case in which the second moment of P(kout ) in the network is finite. These values of τ and α are extremely universal and robust; they emerge in many different types of propagation processes such as directed percolation, CP, VOT, SIS, SIR, and many others, as long as the underlying pattern of connections is either a high-dimensional lattice or a sufficiently homogeneous network [23,27,28,29,30].1. The study consists in extensive numerical simulations, combined with analytical arguments, of the various avalanche models on a variety of networks, both synthetic and real
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
