Cluster synchronization in multiplex networks

¹ Complex Systems Lab, Discipline of Physics, Indian Institute of Technology Indore - Khandwa Road, Simrol, Indore 452020, India
² Centre for Biosciences and Biomedical Engineering, Indian Institute of Technology Indore Khandwa Road, Simrol, Indore 452020, India

^(a) sarikajalan9@gmail.com (corresponding author)

Received: 22 November 2015
Accepted: 1 February 2016

Abstract

We study the impact of the interaction of nodes in a layer of a multiplex network on the dynamical behavior and cluster synchronization of these nodes in the other layers. We find that nodes interactions in one layer affect the cluster synchronizability of the other layer in many different ways. While the multiplexing of a sparse network with the other sparse networks enhances the cluster synchronizability of the individual layer, multiplexing with dense networks suppresses the cluster synchronizability with the network architecture deciding the impact of the enhancement and the suppression. Additionally, at weak couplings the enhancement in the cluster synchronizability, due to multiplexing, remains of the driven type, while for strong couplings the multiplexing may lead to a transition to the self-organized mechanism. The results presented here have applicability in regulating the synchronizability of a particular layer of real-world systems having multiplex architecture.