**Name:**

iaf_tum_2000 - Leaky integrate-and-fire neuron model with exponential

PSCs.

**Description:**

iaf_tum_2000 is an implementation of a leaky integrate-and-fire model

with exponential shaped postsynaptic currents (PSCs) according to [1].

The postsynaptic currents have an infinitely short rise time.

In particular, this model allows setting an absolute and relative

refractory time separately, as required by [1].

The threshold crossing is followed by an absolute refractory period

(t_ref_abs) during which the membrane potential is clamped to the resting

potential. During the total refractory period (t_ref_tot), the membrane

potential evolves, but the neuron will not emit a spike, even if the

membrane potential reaches threshold. The total refractory time must be

larger or equal to the absolute refractory time. If equal, the

refractoriness of the model if equivalent to the other models of NEST.

The linear subthreshold 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_abs double - Duration of absolute refractory period (V_m = V_reset)

in ms.

t_ref_tot double - Duration of total refractory period (no spiking) 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).

**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.

**Author:**

Moritz Helias

**FirstVersion:**

March 2006

**Source:**

/home/graber/work-nest/nest-git/nest-simulator/models/iaf_tum_2000.h