Enhancing relay synchronization in multiplex networks by repulsive relay layer

Abstract

Relay synchronization, which is the interlayer synchronization of two indirectly connected layers, is an important phenomenon in multiplex networks. In this study, relay synchronization is investigated through a triplex network of Hindmarsh-Rose neurons while considering attractive and repulsive intralayer couplings. Relay synchronization is improved when the remote layers have attractive coupling, and the relay layer has repulsive coupling. The essential conditions for the local stability of relay synchronization is found within the framework of master stability function approach. The analytical results are supported by numerical data on synchronization error. Furthermore, enhanced relay synchronization is also shown for larger networks and different internal couplings. Finally, the generalizability of the outcome is confirmed by investigating a triplex network of R"ossler systems.