posted on 2017-12-19, 10:14authored byJames P. Gleeson, Rick Durrett
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.
Funding
PI: MARK LEISING/CLEMSON UNIVERSITY U.S. INTEGRAL USERS GROUP CHAIR SUMMARY: TO SUPPORT MY WORK AND TRAVEL AS CHAIR OF THE U.S. INTEGRAL USERS GROUP (US-IUG). ORGANIZE AND ATTEND 2 US-LUG MEETINGS AT GODDARD SPACE FLIGHT CENTER WORK WITH THE PROJECT TO EN
Dynamics of the metabolic state in the context of a systematic approach to the study of the processes of growth and development of higher plants and fungi