Multiple resource demands and viability in multiplex networks
  Many complex systems demand manifold resources to be supplied from distinct channels to function properly, i.e, water, gas, and electricity for a city. Here, we study a model for viability of such systems demanding more than one type of vital resources produced and distributed by resource nodes in multiplex networks. We found a rich variety of behaviors such as discontinuity, bistability, and hysteresis in the fraction of viable nodes with respect to the density of networks and the fraction of resource nodes. Our result suggests that viability in multiplex networks is not only exposed to the risk of abrupt collapse but also suffers excessive complication in recovery. 
Byungjoon Min and K.-I. Goh
physics.soc-ph cond-mat.stat-mech