  The chimera state with co-existing coherent-incoherent dynamics has recently
attracted a lot of attention due to its wide applicability. We investigate
non-locally coupled identical chaotic maps with delayed interactions in the
multiplex network framework and find that an interplay of delay and
multiplexing brings about an enhanced or suppressed appearance of chimera state
depending on the distribution as well as the parity of delay values in the
layers. Additionally, we report a layer chimera state with an existence of one
layer displaying coherent and another layer demonstrating incoherent dynamical
evolution. The rich variety of dynamical behavior demonstrated here can be used
to gain further insight into the real-world networks which inherently possess
such multi-layer architecture with delayed interactions.
