aeif_cond_exp

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.

References

See also

iaf_cond_exp, aeif_cond_alpha

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 (aka 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

Threshold Potential

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

is_refractory

boolean

false

Equations

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

Source code

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

Characterisation

Synaptic response

aeif_cond_exp_neuron

f-I curve

aeif_cond_exp_neuron