iaf_neuron

Command: iaf_neuron


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.

Author
September 1999 Diesmann Gewaltig
Sends
SpikeEvent

Receives
SpikeEvent CurrentEvent DataLoggingRequest

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.

File
models/iaf_neuron.h
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_Neruons_Singularity.ipynb in
the NEST source code (docs/model_details).