Eur. Phys. J. B (2013) 86: 12
https://doi.org/10.1140/epjb/e2012-31026-x

Regular Article

Networks of noisy oscillators with correlated degree and frequency dispersion

¹ Department of Physics, Humboldt-Universität zu Berlin, Newtonstrasse 15, 12489 Berlin, Germany
² Bernstein Center for Computational Neuroscience Berlin, Philippstrasse 13, 10115 Berlin, Germany
³ Departament de Química Física, Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Spain

^a e-mail: sonne@physik.hu-berlin.de

Received: 3 September 2012
Received in final form: 14 November 2012
Published online: 16 January 2013

Abstract

We investigate how correlations between the diversity of the connectivity of networks and the dynamics at their nodes affect the macroscopic behavior. In particular, we study the synchronization transition of coupled stochastic phase oscillators that represent the node dynamics. Crucially in our work, the variability in the number of connections of the nodes is correlated with the width of the frequency distribution of the oscillators. By numerical simulations on Erdös-Rényi networks, where the frequencies of the oscillators are Gaussian distributed, we make the counterintuitive observation that an increase in the strength of the correlation is accompanied by an increase in the critical coupling strength for the onset of synchronization. We further observe that the critical coupling can solely depend on the average number of connections or even completely lose its dependence on the network connectivity. Only beyond this state, a weighted mean-field approximation breaks down. If noise is present, the correlations have to be stronger to yield similar observations.