The European Physical Journal Special Topics

, Volume 222, Issue 10, pp 2517–2529 | Cite as

Excitable elements controlled by noise and network structure

  • B. SonnenscheinEmail author
  • M.A. Zaks
  • A.B. Neiman
  • L. Schimansky-Geier
Regular Article Nonlinear Dynamics of Stochastic Systems


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.


Hopf Bifurcation Coupling Strength European Physical Journal Special Topic Degree Distribution Noise Intensity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© EDP Sciences and Springer 2013

Authors and Affiliations

  • B. Sonnenschein
    • 1
    • 2
    Email author
  • M.A. Zaks
    • 3
  • A.B. Neiman
    • 4
  • L. Schimansky-Geier
    • 1
    • 2
  1. 1.Department of PhysicsHumboldt-Universität zu BerlinBerlinGermany
  2. 2.Bernstein Center for Computational Neuroscience BerlinBerlinGermany
  3. 3.Institute of Mathematics, Humboldt-Universität zu BerlinBerlinGermany
  4. 4.Department of Physics and AstronomyOhio UniversityAthensUSA

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