  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.
