Enhancing relay synchronization in multiplex networks by repulsive relay layer

¹ School of Mathematics and Physics, China University of Geosciences - Wuhan, 430074, China
² Data Recovery Key Laboratory of Sichuan Province, College of Mathematics and Information Science, Neijiang Normal University - Neijiang, 641100, China
³ Centre for Computational Modelling, Chennai Institute of Technology - Chennai 600069, Tamil Nadu, India
⁴ Centre for Nonlinear Systems, Chennai Institute of Technology - Chennai 600069, Tamil Nadu, India
⁵ Health Technology Research Institute, Amirkabir University of Technology (Tehran Polytechnic) - Tehran, Iran
⁶ Department of Biomedical Engineering, Amirkabir University of Technology (Tehran Polytechnic) - Tehran, Iran

Received: 14 November 2023
Accepted: 19 January 2024

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 generality of the results is confirmed by investigating a triplex network of Rössler systems.