iaf_psc_delta - Leaky integrate-and-fire neuron model.

iaf_psc_delta is an implementation of a leaky integrate-and-fire model
where the potential jumps on each spike arrival.

The threshold crossing is followed by an absolute refractory period
during which the membrane potential is clamped to the resting potential.

Spikes arriving while the neuron is refractory, are discarded by
default. If the property "refractory_input" is set to true, such
spikes are added to the membrane potential at the end of the
refractory period, dampened according to the interval between
arrival and end of refractoriness.

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_psc_delta 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.


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 - Capacitance 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.
I_e double - Constant input current in pA.
V_min double - Absolute lower value for the membrane potential in mV

refractory_input bool - If true, do not discard input during
refractory period. Default: false.

SpikeEvent, CurrentEvent, DataLoggingRequest  

Author: September 1999, Diesmann, Gewaltig


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_delta will probably
address the problem of efficient usage of appropriate vector and
matrix objects.

[1] Rotter S & Diesmann M (1999) Exact digital simulation of time-invariant
linear systems with applications to neuronal modeling. Biologial Cybernetics
[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.

SeeAlso: Source: