https://doi.org/10.1140/epjst/e2013-02034-7
Regular Article
Excitable elements controlled by noise and network structure
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 Institute of Mathematics, Humboldt-Universität zu Berlin, Rudower Chaussee 25, 12489 Berlin, Germany
4 Department of Physics and Astronomy, Ohio University, Athens, Ohio 45701, USA
a e-mail: sonne@physik.hu-berlin.de
Received: 16 July 2013
Revised: 13 August 2013
Published online: 28 October 2013
We study collective dynamics of complex networks of stochastic excitable elements, active rotators. In the thermodynamic limit of infinite number of elements, we apply a mean-field theory for the network and then use a Gaussian approximation to obtain a closed set of deterministic differential equations. These equations govern the order parameters of the network. We find that a uniform decrease in the number of connections per element in a homogeneous network merely shifts the bifurcation thresholds without producing qualitative changes in the network dynamics. In contrast, heterogeneity in the number of connections leads to bifurcations in the excitable regime. In particular we show that a critical value of noise intensity for the saddle-node bifurcation decreases with growing connectivity variance. The corresponding critical values for the onset of global oscillations (Hopf bifurcation) show a non-monotone dependency on the structural heterogeneity, displaying a minimum at moderate connectivity variances.
© EDP Sciences, Springer-Verlag, 2013
