aeif_cond_exp_neuron

aeif_cond_exp - Conductance based exponential integrate-and-fire neuron model

Description

aeif_cond_exp is the adaptive exponential integrate and fire neuron according to Brette and Gerstner (2005), with post-synaptic conductances in the form of truncated exponentials.

The membrane potential is given by the following differential equation:

\[\begin{split}C_m \frac{dV_m}{dt} = -g_L(V_m-E_L)+g_L\Delta_T\exp\left(\frac{V_m-V_{th}}{\Delta_T}\right) - g_e(t)(V_m-E_e) \\ -g_i(t)(V_m-E_i)-w +I_e\end{split}\]

and

\[\tau_w \frac{dw}{dt} = a(V_m-E_L) - w\]

Note that the membrane potential can diverge to positive infinity due to the exponential term. To avoid numerical instabilities, instead of \(V_m\), the value \(\min(V_m,V_{peak})\) is used in the dynamical equations.

Note

The default refractory period for aeif models is zero, consistent with the model definition in Brette & Gerstner [1]. Thus, an aeif neuron with default parameters can fire multiple spikes in a single time step, which can lead to exploding spike numbers and extreme slow-down of simulations. To avoid such unphysiological behavior, you should set a refractory time refr_t > 0.

References

[1]

Brette R and Gerstner W (2005). Adaptive exponential integrate-and-fire model as an effective description of neuronal activity. Journal of Neurophysiology. 943637-3642 DOI: https://doi.org/10.1152/jn.00686.2005

See also

iaf_cond_exp, aeif_cond_alpha

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
C_m	pF	281.0pF	membrane parametersMembrane capacitance
refr_T	ms	2ms	Duration of refractory period
V_reset	mV	-60.0mV	Reset potential
g_L	nS	30.0nS	Leak conductance
E_L	mV	-70.6mV	Leak reversal potential (a.k.a. resting potential)
a	nS	4nS	spike adaptation parametersSubthreshold adaptation
b	pA	80.5pA	Spike-triggered adaptation
Delta_T	mV	2.0mV	Slope factor
tau_w	ms	144.0ms	Adaptation time constant
V_th	mV	-50.4mV	Spike initiation threshold
V_peak	mV	0mV	Spike detection threshold
E_exc	mV	0mV	synaptic parametersExcitatory reversal potential
tau_syn_exc	ms	0.2ms	Synaptic Time Constant excitatory synapse
E_inh	mV	-85.0mV	Inhibitory reversal potential
tau_syn_inh	ms	2.0ms	Synaptic time constant for inhibitory synapse
I_e	pA	0pA	constant external input current

State variables

Name	Physical unit	Default value	Description
V_m	mV	E_L	Membrane potential
w	pA	0pA	Spike-adaptation current
refr_t	ms	0ms	Refractory period timer

Equations

\[\frac{ dV_{m} } { dt }= \frac 1 { C_{m} } \left( { (-g_{L} \cdot (V_{bounded} - E_{L}) + I_{spike} - I_{syn,exc} - I_{syn,inh} - w + I_{e} + I_{stim}) } \right)\]

\[\frac{ dw } { dt }= \frac 1 { \tau_{w} } \left( { (a \cdot (V_{bounded} - E_{L}) - w) } \right)\]

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

Source code

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

Synaptic response

Response to pulse current injection

f-I curve