Original Research ARTICLE

Front. Neuroinform., 15 July 2011 | http://dx.doi.org/10.3389/fninf.2011.00006

On the influence of amplitude on the connectivity between phases

  • Research Institute MOVE, VU University Amsterdam, Amsterdam, Netherlands

In recent studies, functional connectivities have been reported to display characteristics of complex networks that have been suggested to concur with those of the underlying structural, i.e., anatomical, networks. Do functional networks always agree with structural ones? In all generality, this question can be answered with “no”: for instance, a fully synchronized state would imply isotropic homogeneous functional connections irrespective of the “real” underlying structure. A proper inference of structure from function and vice versa requires more than a sole focus on phase synchronization. We show that functional connectivity critically depends on amplitude variations, which implies that, in general, phase patterns should be analyzed in conjunction with the corresponding amplitude. We discuss this issue by comparing the phase synchronization patterns of interconnected Wilson–Cowan models vis-à-vis Kuramoto networks of phase oscillators. For the interconnected Wilson–Cowan models we derive analytically how connectivity between phases explicitly depends on the generating oscillators’ amplitudes. In consequence, the link between neurophysiological studies and computational models always requires the incorporation of the amplitude dynamics. Supplementing synchronization characteristics by amplitude patterns, as captured by, e.g., spectral power in M/EEG recordings, will certainly aid our understanding of the relation between structural and functional organizations in neural networks at large.

Keywords: connectivity, phase synchronization, Kuramoto network, Wilson–Cowan model, amplitude dependency

Citation: Daffertshofer A and van Wijk BCM (2011) On the influence of amplitude on the connectivity between phases. Front. Neuroinform. 5:6. doi: 10.3389/fninf.2011.00006

Received: 30 May 2011; Accepted: 20 June 2011;
Published online: 15 July 2011.

Edited by:

Olaf Sporns, Indiana University, USA

Reviewed by:

Joana R. B. Cabral, Universitat Pompeu Fabra, Spain
Juergen Kurths, Humboldt Universität, Germany

Copyright: © 2011 Daffertshofer and van Wijk. This is an open-access article subject to a non-exclusive license between the authors and Frontiers Media SA, which permits use, distribution and reproduction in other forums, provided the original authors and source are credited and other Frontiers conditions are complied with.

*Correspondence: Andreas Daffertshofer, Research Institute MOVE, VU University Amsterdam, Van der Boechorststraat 9, 1081 BT Amsterdam, Netherlands. e-mail: a.daffertshofer@vu.nl