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arXiv · 2510.09341

Triadic percolation on multilayer networks

Hanlin Sun·Filippo Radicchi·Ginestra Bianconi
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Abstract

Triadic interactions are special types of higher-order interactions that occur when regulator nodes modulate the interactions between other two or more nodes. In presence of triadic interactions, a percolation process occurring on a single-layer network becomes a fully-fledged dynamical system, characterized by period-doubling and a route to chaos. Here, we generalize the model to multilayer networks and name it as the multilayer triadic percolation (MTP) model. We find a much richer dynamical behavior of the MTP model than its single-layer counterpart. MTP displays a Neimark-Sacker bifurcation, leading to oscillations of arbitrarily large period or pseudo-periodic oscillations. Moreover, MTP admits period-two oscillations without negative regulatory interactions, whereas single-layer systems only display discontinuous hybrid transitions. This comprehensive model offers new insights on the importance of regulatory interactions in real-world systems such as brain networks, climate, and ecological systems.

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Hanlin Sun, Filippo Radicchi, Ginestra Bianconi. 2026-02-02. Triadic percolation on multilayer networks. https://doi.org/10.1103/yvtg-wnn4

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