Intra-layer synchronization in multiplex networks

¹ Dipartimento di Ingegneria Elettrica, Elettronica e Informatica, University of Catania - Catania, Italy
² Departamento de Física de la Materia Condensada, University of Zaragoza - Zaragoza, Spain
³ Institute for Biocomputation and Physics of Complex Systems (BIFI), University of Zaragoza Zaragoza, Spain

Received: 12 March 2015
Accepted: 16 April 2015

Abstract

We study synchronization of N oscillators indirectly coupled through a medium which is inhomogeneous and has its own dynamics. The system is formalized in terms of a multilayer network, where the top layer is made of disconnected oscillators and the bottom one, modeling the medium, consists of oscillators coupled according to a given topology. The different dynamics of the medium and the top layer is accounted for by including a frequency mismatch between them. We show a novel regime of synchronization as intra-layer coherence does not necessarily require inter-layer coherence. This regime appears under mild conditions on the bottom layer: arbitrary topologies may be considered, provided that they support synchronization of the oscillators of the medium. The existence of a density-dependent threshold as in quorum-sensing phenomena is also demonstrated.