  We present the emergence of chimeras, a state referring to coexistence of
partly coherent, partly incoherent dynamics in networks of identical
oscillators, in a multiplex network consisting of two non-identical layers
which are interconnected. We demonstrate that the parameter range displaying
the chimera state in the homogeneous first layer of the multiplex networks can
be tuned by changing the link density or connection architecture of the same
nodes in the second layer. We focus on the impact of the interconnected second
layer on the enlargement or shrinking of the coupling regime for which chimeras
are displayed in the homogeneous first layer. We find that a denser homogeneous
second layer promotes chimera in a sparse first layer, where chimeras do not
occur in isolation. Furthermore, while a dense connection density is required
for the second layer if it is homogeneous, this is not true if the second layer
is inhomogeneous. We demonstrate that a sparse inhomogeneous second layer which
is common in real-world complex systems can promote chimera states in a sparse
homogeneous first layer.
