**Name:**

iaf_neuron - Leaky integrate-and-fire neuron model.

**Description:**

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

with alpha-function shaped synaptic currents. Thus, synaptic currents

and the resulting post-synaptic potentials have a finite rise time.

The threshold crossing is followed by an absolute refractory period

during which the membrane potential is clamped to the resting potential.

The subthreshold membrane potential dynamics are given by [3]

dV_m/dt = - ( V_m - E_L ) / tau_m + I_syn(t) / C_m + I_e / C_m

where I_syn(t) is the sum of alpha-shaped synaptic currents

I_syn(t) = Sum[w_j alpha(t-t_j) for t_j in input spike times]

w_j is the synaptic weight of the connection through which the spike

at time t_j arrived. Each individual alpha-current is given by

alpha(t) = e * t/tau_s * e^{-t/tau_s} * Heaviside(t)

alpha(t=tau_s) == 1 is the maximum of the alpha-current.

The linear subthresold dynamics is integrated by the Exact

Integration scheme [1]. 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

[1]. A flow chart can be found in [2].

Critical tests for the formulation of the neuron model are the

comparisons of simulation results for different computation step

sizes. sli/testsuite/nest contains a number of such tests.

The iaf_neuron is the standard model used to check the consistency

of the nest simulation kernel because it is at the same time complex

enough to exhibit non-trivial dynamics and simple enough to compute

relevant measures analytically.

**Parameters:**

The following parameters can be set in the status dictionary.

V_m double - Membrane potential in mV

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.

t_ref double - Duration of refractory period in ms.

V_th double - Spike threshold in mV.

V_reset double - Reset potential of the membrane in mV.

tau_syn double - Rise time of the excitatory synaptic alpha function in ms.

I_e double - Constant external input current in pA.

**Receives:**

SpikeEvent, CurrentEvent, DataLoggingRequest

Author: September 1999, Diesmann, Gewaltig

**Sends:**

SpikeEvent

**Remarks:**

If tau_m is very close to tau_syn, the model will numerically behave as if

tau_m is equal to tau_syn to avoid numerical instabilities.

For details, please see IAF_Neruons_Singularity.ipynb in

the NEST source code (docs/model_details).

**References:**

[1] Rotter S & Diesmann M (1999) Exact simulation of time-invariant linear

systems with applications to neuronal modeling. Biologial Cybernetics

81:381-402.

[2] 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.

[3] Morrison A, Straube S, Plesser H E, & Diesmann M (2007) Exact subthreshold

integration with continuous spike times in discrete time neural network

simulations. Neural Computation 19:47-79.

**SeeAlso:**

**Source:**

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