Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2004-03-17
Phys. Rev. E 70 (2004) 066107
Physics
Condensed Matter
Disordered Systems and Neural Networks
19 pages, 2 figures: accepted in Phys. Rev. E with minor changes
Scientific paper
10.1103/PhysRevE.70.066107
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.
No associations
LandOfFree
Dynamical mean-filed approximation to small-world networks of spiking neurons: From local to global, and/or from regular to random couplings does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Dynamical mean-filed approximation to small-world networks of spiking neurons: From local to global, and/or from regular to random couplings, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Dynamical mean-filed approximation to small-world networks of spiking neurons: From local to global, and/or from regular to random couplings will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-151704