Interplay of delay and multiplexing: Impact on cluster synchronization

Communication delays and multiplexing are ubiquitous features of real-world network systems. We here introduce a simple model where these two features are simultaneously present and report the rich phenomenology which is actually due to their interplay on cluster synchronization. A delay in one layer has non trivial impacts on the collective dynamics of the other layers, enhancing or suppressing synchronization. At the same time, multiplexing may also enhance cluster synchronization of delayed layers. We elucidate several nontrivial (and anti-intuitive) scenarios, which are of interest and potential application in various real-world systems, where the introduction of a delay may render synchronization of a layer robust against changes in the properties of the other layers.