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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
Summary
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.
- 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.
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