Command: iaf_psc_exp


iaf_psc_expp 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. If the
corresponding current event is connected with port 1 the current
is filtered by the synapse (using the time constant of post-synaptic
excitatory currents)

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].


The following parameters can be set in the status dictionary.

E_L double - Resting membrane potential in mV.
C_m double - Capacity of the membrane in pF
tau_m double - Membrane time constant in ms.
tau_syn_ex double - Time constant of postsynaptic excitatory currents in ms
tau_syn_in double - Time constant of postsynaptic inhibitory currents in ms
t_ref double - Duration of refractory period (V_m = V_reset) in ms.
V_m double - Membrane potential in mV
V_th double - Spike threshold in mV.
V_reset double - Reset membrane potential after a spike in mV.
I_e double - Constant input current in pA.
t_spike double - Point in time of last spike in ms.

Moritz Helias

SpikeEvent CurrentEvent DataLoggingRequest


[1] Misha Tsodyks Asher Uziel and Henry Markram (2000) Synchrony Generation in Recurrent
Networks with Frequency-Dependent Synapses The Journal of Neuroscience 2000 Vol. 20 RC50 p.
[2] Rotter S & Diesmann M (1999) Exact simulation of time-invariant linear
systems with applications to neuronal modeling. Biologial Cybernetics
[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.


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_Neruons_Singularity.ipynb in the
NEST source code (docs/model_details).