Warning

This is A PREVIEW for NEST 3.0 and NOT an OFFICIAL RELEASE! Some functionality may not be available and information may be incomplete!

iaf_psc_alpha – Leaky integrate-and-fire neuron model

Description

iaf_psc_alpha is an implementation of a leaky integrate-and-fire model with alpha-function shaped synaptic currents. Thus, synaptic currents and the resulting postsynaptic 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 linear subthreshold 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_psc_alpha 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 compute relevant measures analytically.

Note

The present implementation uses individual variables for the components of the state vector and the non-zero matrix elements of the propagator. Because the propagator is a lower triangular matrix, no full matrix multiplication needs to be carried out and the computation can be done “in place”, i.e. no temporary state vector object is required.

The template support of recent C++ compilers enables a more succinct formulation without loss of runtime performance already at minimal optimization levels. A future version of iaf_psc_alpha will probably address the problem of efficient usage of appropriate vector and matrix objects.

Note

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 implementation details see the IAF_neurons_singularity notebook.

Parameters

The following parameters can be set in the status dictionary.

V_m

mV

Membrane potential

E_L

mV

Resting membrane potential

C_m

pF

Capacity of the membrane

tau_m

ms

Membrane time constant

t_ref

ms

Duration of refractory period

V_th

mV

Spike threshold

V_reset

mV

Reset potential of the membrane

tau_syn_ex

ms

Rise time of the excitatory synaptic alpha function

tau_syn_in

ms

Rise time of the inhibitory synaptic alpha function

I_e

pA

Constant input current

V_min

mV

Absolute lower value for the membrane potenial

References

1(1,2)

Rotter S, Diesmann M (1999). Exact simulation of time-invariant linear systems with applications to neuronal modeling. Biologial Cybernetics 81:381-402. DOI: https://doi.org/10.1007/s004220050570

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. DOI: https://doi.org/10.1016/S0925-2312(01)00409-X

3

Morrison A, Straube S, Plesser H E, Diesmann M (2006). Exact subthreshold integration with continuous spike times in discrete time neural network simulations. Neural Computation, in press DOI: https://doi.org/10.1162/neco.2007.19.1.47

Sends

SpikeEvent

Receives

SpikeEvent, CurrentEvent, DataLoggingRequest