iaf_psc_delta_neuron

iaf_psc_delta - Current-based leaky integrate-and-fire neuron model with delta-kernel post-synaptic currents

Description

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 with_refr_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 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].

References

[1]

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

See also

iaf_psc_alpha, iaf_psc_exp

Copyright statement

This file is part of NEST.

Copyright (C) 2004 The NEST Initiative

NEST is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 2 of the License, or (at your option) any later version.

NEST is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with NEST. If not, see <http://www.gnu.org/licenses/>.

Parameters

Name	Physical unit	Default value	Description
tau_m	ms	10ms	Membrane time constant
C_m	pF	250pF	Capacity of the membrane
refr_T	ms	2ms	Duration of refractory period
E_L	mV	-70mV	Resting membrane potential
V_reset	mV	-70mV	Reset potential of the membrane
V_th	mV	-55mV	Spike threshold
I_e	pA	0pA	constant external input current

State variables

Name	Physical unit	Default value	Description
V_m	mV	E_L	Membrane potential
refr_t	ms	0ms	Refractory period timer

Equations

\[\frac{ dV_{m} } { dt }= \frac{ -(V_{m} - E_{L}) } { \tau_{m} } + \text{convolve}(K_{\delta}, spikes) \cdot (\frac{ \mathrm{mV} } { \mathrm{ms} }) + \frac 1 { C_{m} } \left( { (I_{e} + I_{stim}) } \right)\]

\[\frac{ drefr_{t} } { dt }= \frac{ -1000.0 \cdot \mathrm{ms} } { \mathrm{s} }\]

Source code

The model source code can be found in the NESTML models repository here: iaf_psc_delta_neuron.

Synaptic response

Response to pulse current injection

f-I curve