  We study remote (or relay) synchronization in multilayer networks between
parts of one layer and their counterparts in a second layer, where these two
layers are not directly connected. A simple realization of such a system is a
triplex network where a relay layer in the middle, which is generally not
synchronized, acts as a transmitter between two outer layers. We establish time
delay in the inter-layer coupling as a powerful tool to control various partial
synchronization patterns, in particular chimera states, i.e., complex patterns
of coexisting coherent and incoherent domains. We demonstrate that the
three-layer structure of the network allows for synchronization of the coherent
domains of chimera states in the first layer with their counterparts in the
third layer, whereas the incoherent domains either remain desynchronized or
synchronized. By varying the topology of the relay layer, we study its
influence on the remote synchronization in the outer layers. As model dynamics
we use the paradigmatic FitzHugh-Nagumo system.
