Threshold cascades with response heterogeneity in multiplex networks

Kyu Min Lee, Charles D. Brummitt, K. I. Goh

Research output: Contribution to journalArticlepeer-review

90 Citations (Scopus)


Threshold cascade models have been used to describe the spread of behavior in social networks and cascades of default in financial networks. In some cases, these networks may have multiple kinds of interactions, such as distinct types of social ties or distinct types of financial liabilities; furthermore, nodes may respond in different ways to influence from their neighbors of multiple types. To start to capture such settings in a stylized way, we generalize a threshold cascade model to a multiplex network in which nodes follow one of two response rules: some nodes activate when, in at least one layer, a large enough fraction of neighbors is active, while the other nodes activate when, in all layers, a large enough fraction of neighbors is active. Varying the fractions of nodes following either rule facilitates or inhibits cascades. Near the inhibition regime, global cascades appear discontinuously as the network density increases; however, the cascade grows more slowly over time. This behavior suggests a way in which various collective phenomena in the real world could appear abruptly yet slowly.

Original languageEnglish
Article number062816
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number6
Publication statusPublished - 2014 Dec 29

Bibliographical note

Publisher Copyright:
© 2014 American Physical Society.

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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