noise_generator - Device to generate Gaussian white noise current.
This device can be used to inject a Gaussian "white" noise current into a node.
The current is not really white, but a piecewise constant current with Gaussian
distributed amplitude. The current changes at intervals of dt. dt must be a
multiple of the simulation step size, the default is 1.0ms,
corresponding to a 1kHz cut-off.
Additionally a second sinusodial modulated term can be added to the standard
deviation of the noise.
The current generated is given by
@f[ I(t) = mean + std * N_j \text{ for } t_0 + j dt <= t < t_0 + (j-1) dt @f]
where \f$ N_j \f$ are Gaussian random numbers with unit standard deviation and
\f$ t_0 \f$ is the device onset time.
If the modulation is added the current is given by
@f[
I(t) = mean + \sqrt(std^2 + std_{mod}^2 * \sin(\omega * t + phase)) * N_j \\
\text{ for } t_0 + j dt <= t < t_0 + (j-1) dt
@f]
For a detailed discussion of the properties of the noise generator, please see
the noise_generator.ipynb notebook included in the NEST source code
(docs/model_details).
The following parameters can be set in the status dictionary:
\verbatim embed:rst
========== ====== =========================================================
mean pA Mean value of the noise current
std pA Standard deviation of noise current
dt ms Interval between changes in current, default 1.0ms
std_mod pA Modulated standard deviation of noise current
phase real Phase of sine modulation (0-360 deg)
frequency Hz Frequency of sine modulation
========== ====== =========================================================
\endverbatim
CurrentEvent
• All targets receive different currents.
• The currents for all targets change at the same points in time.
• The interval between changes, dt, must be a multiple of the time step.
• The effect of this noise current on a neuron DEPENDS ON DT. Consider
the membrane potential fluctuations evoked when a noise current is
injected into a neuron. The standard deviation of these fluctuations
across an ensemble will increase with dt for a given value of std.
For the leaky integrate-and-fire neuron with time constant \f$ \tau_m \f$ and
capacity \f$ C_m \f$, membrane potential fluctuations Sigma at time
s \f$ t_j+delay \f$ are given by
@f[
\Sigma = std * \tau_m / C_m * \sqrt( (1-x) / (1+x) ) \\
\text{where } x = exp(-dt/\tau_m)
@f]
for large \f$ t_j \f$. In the white noise limit, dt -> 0, one has
@f[
\Sigma -> std / C_m * \sqrt(dt * \tau / 2).
@f]
To obtain comparable results for different values of dt, you must
adapt std.
• As the noise generator provides a different current for each of its targets,
the current recorded represents the instantaneous average of all the
currents computed. When there exists only a single target, this would be
equivalent to the actual current provided to that target.
Ported to NEST2 API 08/2007 by Jochen Eppler, updated 07/2008 by HEP
/var/www/debian/nest/nest-simulator-2.20.0/models/noise_generator.h