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Area of Science:

  • Complex systems
  • Network science
  • Statistical physics

Background:

  • Avalanches or cascades are chain reactions where one event triggers subsequent events.
  • Studying average avalanche shapes (temporal profiles) is crucial for understanding these dynamics.
  • At criticality, rescaled average avalanche shapes for varying durations collapse onto a universal curve.

Purpose of the Study:

  • To derive an equation for average avalanche shape in cascade dynamics on networks using Markov branching process theory.
  • To analyze the conditions leading to non-symmetric average avalanche shapes at criticality.
  • To propose experimental methods for identifying critical states in cascading systems.

Main Methods:

  • Application of Markov branching process theory.
  • Mathematical derivation of an equation for average avalanche shape.
  • Numerical simulations of information spreading, neural dynamics, and behavior adoption models.

Main Results:

  • A derived equation governs average avalanche shape for cascade dynamics on networks.
  • Nonsymmetric average avalanche shapes are predicted at criticality for specific dynamics and network topologies.
  • The study provides examples from information spreading, neural dynamics, and behavior adoption.

Conclusions:

  • The derived theory explains observed nonsymmetric avalanche shapes in experimental data.
  • The findings offer a theoretical framework for analyzing critical phenomena in diverse cascading systems.
  • Simple experimental tests are proposed to detect criticality in real-world systems.