Asymmetric dual-threshold bootstrap percolation on random hypergraphs
TL;DR
This work shows that a dual-threshold bootstrap percolation model on random hypergraphs separates a connected active backbone from large-scale endogenous activation, providing a basis for predicting cascade risk and designing targeted node- and group-level interventions in complex systems.
Abstract
Collective behaviors such as infrastructure failures and social adoption propagate through groups governed by fixed quorum requirements rather than by pairwise contacts. However, it remains unclear how absolute group- and individual-level thresholds jointly shape cascades in higher-order networks. Here we show that a dual-threshold bootstrap percolation model on random hypergraphs separates a connected active backbone from large-scale endogenous activation. A seed-driven giant component emerges continuously at a structural percolation threshold, whereas macroscopic amplification ignites only at a higher dynamical tipping point, creating a metastable safety margin in which communication is possible without systemic outbreak. This decoupling reflects an asymmetric division of labor: the group quorum M acts as a source-side filter, while the individual barrier K serves as a receiver-side gatekeeper. On homogeneous substrates, the structural onset is protected to leading order against K , but heterogeneous connectivity erodes this protection. Our framework provides a basis for predicting cascade risk and designing targeted node- and group-level interventions in complex systems.