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Triadic percolation on multilayer networks.

Hanlin Sun1, Filippo Radicchi2, Ginestra Bianconi3

  • 1Stockholm University, KTH Royal Institute of Technology, Nordita, Hannes Alfvéns väg 12, SE-106 91 Stockholm, Sweden.

Physical Review. E
|February 20, 2026
PubMed
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The multilayer triadic percolation (MTP) model reveals complex dynamics in regulatory networks. This model shows richer behaviors like Neimark-Sacker bifurcations and period-two oscillations, crucial for understanding real-world systems.

Area of Science:

  • Complex Systems Science
  • Network Science
  • Dynamical Systems Theory

Background:

  • Triadic interactions involve regulator nodes modulating pairwise interactions.
  • These interactions transform simple percolation into complex dynamical systems with routes to chaos.

Purpose of the Study:

  • To generalize the single-layer triadic percolation model to multilayer networks.
  • To investigate the novel dynamical behaviors arising in this multilayer context.

Main Methods:

  • Development of the multilayer triadic percolation (MTP) model.
  • Analysis of dynamical system properties, including bifurcations and oscillation types.

Main Results:

  • The MTP model exhibits richer dynamics than single-layer systems.

Related Experiment Videos

  • Observed Neimark-Sacker bifurcations leading to pseudoperiodic oscillations.
  • Period-two oscillations emerge without negative regulatory interactions.

    • Conclusions:

    • Multilayer regulatory interactions significantly enrich network dynamics.
    • The MTP model provides insights into systems like brain networks, climate, and ecology.
    • Understanding these dynamics is vital for complex real-world systems.