Herbert Treutlein and Klaus Schulten.
Noise-induced neural impulses.
European Biophysics Journal, 13:355-365, 1986.
TREU86
The firing pattern of neural pulses often show the following features: the shapes of individual pulses are nearly identical and frequency independent; the firing frequency can vary over a broad range; the time period between pulses shows a stochastic scatter. This behaviour cannot be understood on the basis of a deterministic non-linear dynamic process, e.g. the Bonhoeffer-van der Pol model. We demonstrate in this paper that a noise term added to the Bonhoeffer-van der Pol model can reproduce the firing patterns of neurons very well. For this purpose we have considered the Fokker-Planck equation corresponding to the stochastic Bonhoeffer-van der Pol model. This equation has been solved by a new Monte Carlo algorithm. We demonstrate that the ensuing distribution functions represent only the global characteristics of the underlying force field: lines of zero slope which attract nearby trajectories prove to be the regions of phase space where the distributions concentrate their amplitude. Since there are two such lines the distributions are bimodal representing repeated fluctuations between two lines of zero slope. Even in cases where the deterministic Bonhoeffer-van der Pol model does not show limit cycle behaviour the stochastic system produces a limit cycle. This cycle can be identified with the firing of neural pulses.
Download Full Text
The manuscripts available on our site are provided for your personal
use only and may not be retransmitted or redistributed without written
permissions from the paper's publisher and author. You may not upload any
of this site's material to any public server, on-line service, network, or
bulletin board without prior written permission from the publisher and
author. You may not make copies for any commercial purpose. Reproduction
or storage of materials retrieved from this web site is subject to the
U.S. Copyright Act of 1976, Title 17 U.S.C.