# Reentrant phase transitions in threshold driven contagion on multiplex networks

## TL;DR

This paper demonstrates that threshold driven contagion on multiplex networks with heterogeneous weights can exhibit reentrant phase transitions, remaining susceptible to cascades even at high connectivity levels, explaining large-scale contagion.

## Contribution

It introduces the concept of reentrant phase transitions in threshold contagion models on weighted multiplex networks, revealing new dynamics not seen in single-layer models.

## Key findings

- Multiplex networks with weight heterogeneity can sustain global cascades at any connectivity level.
- Reentrant phase transitions cause alternating phases of stability and instability as edge density increases.
- Large-scale contagion can occur in highly connected, heterogeneous networks, contrary to previous models.

## Abstract

Models of threshold driven contagion explain the cascading spread of information, behavior, systemic risk, and epidemics on social, financial and biological networks. At odds with empirical observation, these models predict that single-layer unweighted networks become resistant to global cascades after reaching sufficient connectivity. We investigate threshold driven contagion on weight heterogeneous multiplex networks and show that they can remain susceptible to global cascades at any level of connectivity, and with increasing edge density pass through alternating phases of stability and instability in the form of reentrant phase transitions of contagion. Our results provide a novel theoretical explanation for the observation of large scale contagion in highly connected but heterogeneous networks.