Regensburg 2004 – scientific programme
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DY: Dynamik und Statistische Physik
DY 42: Long-Range Correlations and Multifractals
DY 42.1: Talk
Thursday, March 11, 2004, 11:30–11:45, H2
Effects of Membrane Potential Slope and Refractoriness on Spike Synchronization — •Sven Goedeke1, Tom Tetzlaff1,2, Theo Geisel1, and Markus Diesmann1,2 — 1MPI für Strömungsforschung und Institut für Nichtlineare Dynamik der Universität Göttingen — 2Neurobiologie und Biophysik, Biologie III, Universität Freiburg
Neuron models based on the instantaneous spiking probability f(t) are a
convenient mathematical tool in the study of neural networks. Often
f is expressed in terms of a state variable, e.g. the membrane
potential u(t). Recent studies [1,2] have applied f(u)-models to
spike synchronization in
feed-forward networks, emphasizing the dominant role of
refractoriness. We show that f(u) is inconsistent with
integrate-and-fire dynamics. An expression exhibiting the dependence
of f on u and its temporal derivative u is derived. We use
a bilinear f(u,u) for an analytical
investigation of feed-forward synchronization.
The system displays bistability and
quantitatively reproduces integrate-and-fire simulation results. The
u-dependence is a powerful mechanism of synchronization, taking
effect prior to refractoriness. The main function of refractoriness is
normalizing the number of spikes.
[1] Gewaltig M-O (2000) Aachen, Germany: Shaker
[2] Kistler WM & Gerstner W (2002) Neural Comput 14:987