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Related Experiment Video

Updated: Apr 18, 2026

Time-dependent Increase in the Network Response to the Stimulation of Neuronal Cell Cultures on Micro-electrode Arrays
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Threshold cascades with response heterogeneity in multiplex networks.

Kyu-Min Lee1, Charles D Brummitt2, K-I Goh1

  • 1Department of Physics and Institute of Basic Science, Korea University, Seoul 136-713, Korea.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 24, 2015
PubMed
Summary

This study generalizes threshold cascade models for multiplex networks. It reveals how different node response rules influence cascade dynamics, showing abrupt yet slow collective phenomena.

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Area of Science:

  • Network Science
  • Complex Systems
  • Sociophysics

Background:

  • Threshold cascade models explain behavior spread in social networks and defaults in financial networks.
  • Real-world networks often feature multiple interaction types (e.g., social ties, financial liabilities) and varied node responses to neighbor influence.

Purpose of the Study:

  • To generalize threshold cascade models to multiplex networks with diverse node response rules.
  • To investigate how varying fractions of nodes with different activation thresholds affect cascade behavior.

Main Methods:

  • Developed a generalized threshold cascade model for multiplex networks.
  • Incorporated two distinct node response rules: activation in at least one layer or activation in all layers.
  • Analyzed cascade dynamics by varying node fractions and network density.

Main Results:

  • Cascade behavior is modulated by the fractions of nodes following each response rule.
  • Near the inhibition regime, global cascades emerge discontinuously with increasing network density.
  • Cascades exhibit slower growth over time in this regime.

Conclusions:

  • The generalized model captures complex cascade dynamics in multiplex networks.
  • Abrupt yet slow collective phenomena observed in real-world systems can be explained by these dynamics.
  • This framework offers insights into emergent behaviors in interconnected systems.