Eur. Phys. J. B (2012) 85: 40
https://doi.org/10.1140/epjb/e2011-20562-6

Regular Article

Three types of synchronisation in complex modular networks

¹ Department of Physics, Southeast University, 210096 Nanjing, P.R. China
² School of Physics and Electronic Engineering, Nanjing Xiaozhuang University, 210017 Nanjing, P.R. China
³ Research Centre Jülich, Institute of Neuroscience and Medicine INM-2, Leo-Brandt-Str., 52425 Jülich, Germany
⁴ Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, 01187 Dresden, Germany

^a e-mail: haijunw@njxzc.edu.cn

Received: 10 July 2011
Received in final form: 1 December 2011
Published online: 23 January 2012

Abstract

We study the synchronisation dynamics in complex modular networks. Through theoretical analysis, three types of synchronisation, i.e. uniform, modular and pattern synchronisation, are identified and necessary conditions for their stabilities are given. Numerical simulations with identical chaotic logistic maps and Lorenz oscillators are given to support the theoretical analysis.