Group dynamics shape contagion onsets and multistable active phases under collective reinforcement

TL;DR

This paper demonstrates that group dynamics critically influence contagion phase transitions, revealing complex behaviors and multistability in systems with time-varying structures, challenging static assumptions.

Contribution

It introduces an analytically tractable model incorporating group turnover, showing how dynamic group composition affects contagion transitions and phase diagrams.

Findings

Time-varying structures can induce discontinuous phase transitions.

Multistable active phases with coexisting states are observed.

Static models may underestimate the nonlinear reinforcement needed for discontinuous transitions.

Abstract

Group-based reinforcement can induce discontinuous transitions from inactive to active phases in higher-order contagion models. However, these results are typically obtained on static interaction structures or within mean-field approximations that neglect temporal changes in group composition. Here, we show that group dynamics is not a secondary effect but a central aspect that determines the macroscopic transition class of higher-order contagion processes. We develop an analytically tractable approximate master equation model that effectively interpolates between quenched and mean-field limits through a group composition turnover rate. Our results reveal the rich impact of time-varying structures: it can induce discontinuous phase transition, broaden the bistable region, and at the same time promote or suppress contagion near criticality. Moreover, when real-world turnover rates and group-size heterogeneity are taken into account, the system exhibits a qualitatively richer phase diagram with four distinct dynamical phases, combining continuous or discontinuous transitions with localized or delocalized activity. In localized regimes, we uncover multistable active phases with multiple coexisting active states, which are observed in neither the annealed nor the quenched limits, and extend classical absorbing-active bistability. Finally, we demonstrate that the emergence of discontinuous transitions in real-world systems requires stronger nonlinear reinforcement than previously thought, indicating that simulations in static structures can yield qualitatively misleading predictions.