2012/08/31 by Bernard Sonnenschein, Francesc Sagués, Lutz Schimansky-Geier
Computer Science · Neuroscience · Physics and Astronomy · #Neural Networks Stability and Synchronization #Neural dynamics and brain function #Nonlinear Dynamics and Pattern Formation #cond-mat.dis-nn #cond-mat.stat-mech #nlin.CD #physics.bio-ph
paper · pdf · doi:10.1140/epjb/e2012-31026-x
published as Eur. Phys. J. B (2013) 86:12 · 6 pages, 2 figures
openalex publication_date 2013/01/01 · arxiv created 2013/01/21 · arxiv updated 2013/01/22 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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.