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For the paper:

Brette R, Guigon E (2003) Reliability of spike timing is a general
property of spiking model neurons. Neural Comput 15:279-308

Abstract:

The responses of neurons to time-varying injected currents are
reproducible on a trial-by-trial basis in vitro, but when a constant
current is injected, small variances in interspike intervals across
trials add up, eventually leading to a high variance in spike
timing. It is unclear whether this difference is due to the nature of
the input currents or the intrinsic properties of the neurons. Neuron
responses can fail to be reproducible in two ways: dynamical noise can
accumulate over time and lead to a desynchronization over trials, or
several stable responses can exist, depending on the initial
condition. Here we show, through simulations and theoretical
considerations, that for a general class of spiking neuron models,
which includes, in particular, the leaky integrate-and-fire model as
well as nonlinear spiking models, aperiodic currents, contrary to
periodic currents, induce reproducible responses, which are stable
under noise, change in initial conditions and deterministic
perturbations of the input. We provide a theoretical explanation for
aperiodic currents that cross the threshold.

Brian simulator models are available at this web page:

<a href="http://briansimulator.org/docs/examples-frompapers_Brette_Guigon_2003.html">http://briansimulator.org/docs/examples-frompapers_Brette_Guigon_2003.html</a>

The simulation reproduces Fig. 10D,E:

<img src="./screenshot.png" alt="screenshot" width="550">

This simulation requires Brian which can be downloaded and installed
from the instructions available at <a href="http://www.briansimulator.org/">http://www.briansimulator.org/</a>

For support on installing and using Brian simulations there is a
support group at <a href="https://groups.google.com/group/briansupport">https://groups.google.com/group/briansupport</a>.
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