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Hierarchical burst model for complex bursty dynamics.

Byoung-Hwa Lee1,2, Woo-Sung Jung1,2,3, Hang-Hyun Jo1,2,4

  • 1Department of Physics, Pohang University of Science and Technology, Pohang 37673, Republic of Korea.

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Summary
This summary is machine-generated.

This study introduces a hierarchical burst model to explain temporal scaling in natural and social phenomena. The model confirms a key scaling relation (α+γ=2) even with interevent time correlations, revealing insights into complex bursty dynamics.

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Area of Science:

  • Complex Systems
  • Statistical Physics
  • Time Series Analysis

Background:

  • Temporal inhomogeneities in natural and social phenomena exhibit scaling behaviors.
  • Characterizations include autocorrelation function decay (exponent γ), interevent time distribution (exponent α), and burst size distributions.
  • Interevent time is the interval between consecutive events; burst size is the number of events within a time window.

Purpose of the Study:

  • To understand temporal scaling behaviors implying a hierarchical temporal structure.
  • To devise a hierarchical burst model based on multilevel causal or decision-making processes.
  • To analyze the scaling relations and emergent properties of such hierarchical structures.

Main Methods:

  • Development of a hierarchical burst model.
  • Analytical and numerical studies of the model.
  • Investigation of autocorrelation functions, interevent time distributions, and burst size distributions.
  • Imposition of event ordering conditions to observe log-periodic behavior.

Main Results:

  • Confirmation of the scaling relation α+γ=2, even with interevent time correlations.
  • Stretched exponential burst size distributions supporting interevent time correlations.
  • Observation of log-periodic behavior in the autocorrelation function under event ordering conditions.

Conclusions:

  • The hierarchical burst model provides a framework for understanding complex bursty dynamics.
  • The model explains observed temporal scaling behaviors and their underlying hierarchical structure.
  • This approach offers insights into the mechanisms driving phenomena with complex temporal patterns.