aeif_psc_exp – Current-based exponential integrate-and-fire neuron model

Description

aeif_psc_exp is the adaptive exponential integrate and fire neuron according to Brette and Gerstner (2005), with postsynaptic currents in the form of truncated exponentials.

This implementation uses the embedded 4th order Runge-Kutta-Fehlberg solver with adaptive stepsize to integrate the differential equation.

The membrane potential is given by the following differential equation:

\[C dV/dt= -g_L(V-E_L)+g_L\cdot\Delta_T\cdot\exp((V-V_T)/\Delta_T) - w(t) + I_{syn}(t) + I_e\]

and

\[\tau_w \cdot dw/dt= a(V-E_L) - w\]
\[I_{syn}(t) ~ \sum_k \exp((t-t^k)/\tau_{syn})H(t - t^k) .\]

Here \(H(t)\) is the Heaviside step function and k indexes incoming spikes.

For implementation details see the aeif_models_implementation notebook.

See also [1].

Parameters

The following parameters can be set in the status dictionary.

Dynamic state variables:

V_m

mV

Membrane potential

I_ex

pA

Excitatory synaptic current

I_in

pA

Inhibitory synaptic current

w

pA

Spike-adaptation current

Membrane Parameters

C_m

pF

Capacity of the membrane

t_ref

ms

Duration of refractory period

V_reset

mV

Reset value for V_m after a spike

E_L

mV

Leak reversal potential

g_L

nS

Leak conductance

I_e

pA

Constant external input current

Spike adaptation parameters

a

ns

Subthreshold adaptation

b

pA

Spike-triggered adaptation

Delta_T

mV

Slope factor

tau_w

ms

Adaptation time constant

V_th

mV

Spike initiation threshold

V_peak

mV

Spike detection threshold

Synaptic parameters

tau_syn_ex

ms

Exponential decay time constant of excitatory synaptic conductance kernel

tau_syn_in

ms

Exponential decay time constant of inhibitory synaptic conductance kernel

Integration parameters

gsl_error_tol

real

This parameter controls the admissible error of the GSL integrator. Reduce it if NEST complains about numerical instabilities

Sends

SpikeEvent

Receives

SpikeEvent, CurrentEvent, DataLoggingRequest

References

See also

Neuron, Integrate-And-Fire, Adaptive Threshold, Current-Based