**Name:**

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

PSCs.

**Description:**

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].

**Parameters:**

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.

**Receives:**

SpikeEvent, CurrentEvent, DataLoggingRequest

**Sends:**

SpikeEvent

**Remarks:**

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].

**References:**

[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

81:381-402.

[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

**Author:**

Moritz Helias

**FirstVersion:**

March 2006

**SeeAlso:**

**Source:**

/home/graber/work-nest/nest-git/nest-simulator/models/iaf_psc_exp.h