Relay synchronization and control of dynamics in multiplex networks with unidirectional interlayer coupling

Multiplex networks provide a proper framework for understanding the dynamics of complex systems with differing types of interactions. This study considers different dynamical states possible in a multiplex network of nonlinear oscillators, with a drive layer and two identical response layers where the interlayer interactions are unidirectional. We report how the directionality in coupling can lead to relay synchronization with amplification in the two response layers through feedback from the middle drive layer. The amplitude of synchronized oscillations of response layers can be controlled by tuning the strength of interlayer coupling. Moreover, we find the synchronization patterns that emerge in the response layers depend on the nature of interlayer coupling, whether feedback or diffusive, and the time scale or parameter mismatches between drive and response layers. Thus, the study indicates the potential for controlling and optimizing the dynamics of response layers remotely by adjusting the strength of interlayer coupling or tuning the dynamic time scale of the drive layer.