  We introduce the sandpile model on multiplex networks with more than one type
of edge and investigate its scaling and dynamical behaviors. We find that the
introduction of multiplexity does not alter the scaling behavior of avalanche
dynamics; the system is critical with an asymptotic power-law avalanche size
distribution with an exponent $\tau = 3/2$ on duplex random networks. The
detailed cascade dynamics, however, is affected by the multiplex coupling. For
example, higher-degree nodes such as hubs in scale-free networks fail more
often in the multiplex dynamics than in the simplex network counterpart in
which different types of edges are simply aggregated. Our results suggest that
multiplex modeling would be necessary in order to gain a better understanding
of cascading failure phenomena of real-world multiplex complex systems, such as
the global economic crisis.
