Blog
About

  • Record: found
  • Abstract: found
  • Article: found
Is Open Access

Dynamical mean-filed approximation to small-world networks of spiking neurons: From local to global, and/or from regular to random couplings

Preprint

Read this article at

Bookmark
      There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

      Abstract

      By extending a dynamical mean-field approximation (DMA) previously proposed by the author [H. Hasegawa, Phys. Rev. E {\bf 67}, 41903 (2003)], we have developed a semianalytical theory which takes into account a wide range of couplings in a small-world network. Our network consists of noisy \(N\)-unit FitzHugh-Nagumo (FN) neurons with couplings whose average coordination number \(Z\) may change from local (\(Z \ll N \)) to global couplings (\(Z=N-1\)) and/or whose concentration of random couplings \(p\) is allowed to vary from regular (\(p=0\)) to completely random (p=1). We have taken into account three kinds of spatial correlations: the on-site correlation, the correlation for a coupled pair and that for a pair without direct couplings. The original \(2 N\)-dimensional {\it stochastic} differential equations are transformed to 13-dimensional {\it deterministic} differential equations expressed in terms of means, variances and covariances of state variables. The synchronization ratio and the firing-time precision for an applied single spike have been discussed as functions of \(Z\) and \(p\). Our calculations have shown that with increasing \(p\), the synchronization is {\it worse} because of increased heterogeneous couplings, although the average network distance becomes shorter. Results calculated by out theory are in good agreement with those by direct simulations.

      Related collections

      Author and article information

      Journal
      16 March 2004
      2004-09-08
      cond-mat/0403415
      10.1103/PhysRevE.70.066107
      Custom metadata
      Phys. Rev. E 70 (2004) 066107
      19 pages, 2 figures: accepted in Phys. Rev. E with minor changes
      cond-mat.dis-nn

      Comments

      Comment on this article