  We investigate solitary states in a two-layer multiplex network of
FitzHugh-Nagumo neurons in the oscillatory regime. We demonstrate how solitary
states can be induced in a multiplex network consisting of two non-identical
layers. More specifically, we show that these patterns can be introduced via
weak multiplexing into a network that is fully synchronized in isolation. We
show that this result is robust under variations of the inter-layer coupling
strength and largely independent of the choice of initial conditions. Moreover,
we study the vulnerability of solitary states with respect to changes in the
inter-layer topology. In more detail, we remove links that connect two solitary
nodes of each layer and evaluate the resulting pattern. We find a highly
non-trivial dependence of the survivability of the solitary states on
topological (position in the network) and dynamical (phase of the oscillation)
characteristics.
