iaf_psc_exp - Leaky integrate-and-fire neuron model with exponential  
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.

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.

SpikeEvent, CurrentEvent, DataLoggingRequest  



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 [4].

[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. 1-5
[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.
[4] Schuecker J, Diesmann M, Helias M (2015) Modulated escape from a
metastable state driven by colored noise.
Physical Review E 92:052119

Moritz Helias 
March 2006  
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