iaf_psc_exp - Leaky integrate-and-fire neuron model with exponential
PSCs.
iaf_psc_exp is an implementation of a leaky integrate-and-fire model
with exponential shaped postsynaptic currents (PSCs) according to [1].
Thus, postsynaptic currents have an infinitely short rise time.
The threshold crossing is followed by an absolute refractory period (t_ref)
during which the membrane potential is clamped to the resting potential
and spiking is prohibited.
The linear subthresold dynamics is integrated by the Exact
Integration scheme [2]. 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
[2]. A flow chart can be found in [3].
Spiking in this model can be either deterministic (delta=0) or stochastic (delta
> 0). In the stochastic case this model implements a type of spike response
model with escape noise [4, 5].
The following parameters can be set in the status dictionary.
\verbatim embed:rst
=========== ======= ========================================================
E_L mV Resting membrane potential
C_m pF Capacity of the membrane
tau_m ms Membrane time constant
tau_syn_ex ms Time constant of postsynaptic excitatory currents
tau_syn_in ms Time constant of postsynaptic inhibitory currents
t_ref ms Duration of refractory period (V_m = V_reset)
V_m mV Membrane potential in mV
V_th mV Spike threshold in mV
V_reset mV Reset membrane potential after a spike
I_e pA Constant input current
t_spike ms Point in time of last spike
=========== ======= ========================================================
\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).
iaf_psc_exp can handle current input in two ways: Current input
through receptor_type 0 are handled as stepwise constant current
input as in other iaf models, i.e., this current directly enters
the membrane potential equation. Current input through
receptor_type 1, in contrast, is filtered through an exponential
kernel with the time constant of the excitatory synapse,
tau_syn_ex. For an example application, see [6].
\verbatim embed:rst
.. [1] Tsodyks M, Uziel A, Markram H (2000). Synchrony generation in recurrent
networks with frequency-dependent synapses. The Journal of Neuroscience,
20,RC50:1-5. URL: https://infoscience.epfl.ch/record/183402
.. [2] 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
.. [3] 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
.. [4] Schuecker J, Diesmann M, Helias M (2015). Modulated escape from a
metastable state driven by colored noise. Physical Review E 92:052119
DOI: https://doi.org/10.1103/PhysRevE.92.052119
\endverbatim
=======
Moritz Helias
March 2006
/var/www/debian/nest/nest-simulator-2.20.0/models/iaf_psc_exp.h