iaf_psc_alpha - Leaky integrate-and-fire neuron model.
iaf_psc_alpha is an implementation of a leaky integrate-and-fire model
with alpha-function shaped synaptic currents. Thus, synaptic currents
and the resulting post-synaptic potentials have a finite rise time.
The threshold crossing is followed by an absolute refractory period
during which the membrane potential is clamped to the resting potential.
The linear subthresold dynamics is integrated by the Exact
Integration scheme [][1]. The neuron dynamics is solved on the time
grid given by the computation step size. Incoming as well as emitted
spikes are forced to that grid.
An additional state variable and the corresponding differential
equation represents a piecewise constant external current.
The general framework for the consistent formulation of systems with
neuron like dynamics interacting by point events is described in
[1]. A flow chart can be found in [2].
Critical tests for the formulation of the neuron model are the
comparisons of simulation results for different computation step
sizes. sli/testsuite/nest contains a number of such tests.
The iaf_psc_alpha is the standard model used to check the consistency
of the nest simulation kernel because it is at the same time complex
enough to exhibit non-trivial dynamics and simple enough compute
relevant measures analytically.
The following parameters can be set in the status dictionary.
\verbatim embed:rst
=========== ====== ==========================================================
V_m mV Membrane potential
E_L mV Resting membrane potenial
C_m pF Capacity of the membrane
tau_m ms Membrane time constant
t_ref ms Duration of refractory period
V_th mV Spike threshold
V_reset mV Reset potential of the membrane
tau_syn_ex ms Rise time of the excitatory synaptic alpha function
tau_syn_in ms Rise time of the inhibitory synaptic alpha function
I_e pA Constant input current
V_min mV Absolute lower value for the membrane potenial
=========== ====== ==========================================================
\endverbatim
SpikeEvent, CurrentEvent, DataLoggingRequest
SpikeEvent
If tau_m is very close to tau_syn_ex or tau_syn_in, the model
will numerically behave as if tau_m is equal to tau_syn_ex or
tau_syn_in, respectively, to avoid numerical instabilities.
For details, please see IAF_neurons_singularity.ipynb in
the NEST source code (docs/model_details).
\verbatim embed:rst
.. [1] Rotter S, Diesmann M (1999). Exact simulation of
time-invariant linear systems with applications to neuronal
modeling. Biologial Cybernetics 81:381-402.
DOI: https://doi.org/10.1007/s004220050570
.. [2] Diesmann M, Gewaltig M-O, Rotter S, & Aertsen A (2001). State
space analysis of synchronous spiking in cortical neural
networks. Neurocomputing 38-40:565-571.
DOI: https://doi.org/10.1016/S0925-2312(01)00409-X
.. [3] Morrison A, Straube S, Plesser H E, Diesmann M (2006). Exact
subthreshold integration with continuous spike times in discrete time
neural network simulations. Neural Computation, in press
DOI: https://doi.org/10.1162/neco.2007.19.1.47
\endverbatim
Diesmann, Gewaltig
September 1999
/var/www/debian/nest/nest-simulator-2.20.0/models/iaf_psc_alpha.h