Warning

This is A PREVIEW for NEST 3.0 and NOT an OFFICIAL RELEASE! Some functionality may not be available and information may be incomplete!

# aeif_psc_delta – Current-based adaptive exponential integrate-and-fire neuron model with delta synapse¶

## Description¶

aeif_psc_delta is the adaptive exponential integrate and fire neuron according to Brette and Gerstner (2005), with postsynaptic currents in the form of delta spikes.

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:

$\begin{split}C dV/dt= -g_L(V-E_L)+g_L*\Delta_T*\exp((V-V_T)/\Delta_T)-g_e(t)(V-E_e) \\ -g_i(t)(V-E_i)-w +I_e\end{split}$

and

$\tau_w * dw/dt= a(V-E_L) -W$
$I(t) = J \sum_k \delta(t - t^k).$

Here delta is the dirac delta function and k indexes incoming spikes. This is implemented such that V_m will be incremented/decremented by the value of J after a spike.

For implementation details see the aeif_models_implementation notebook.

## Parameters¶

The following parameters can be set in the status dictionary.

 Dynamic state variables V_m mV Membrane potential 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 tau_w ms Adaptation time constant Delta_T mV Slope factor tau_w ms Adaptation time constant V_th mV Spike initiation threshold V_peak mV Spike detection threshold
 Integration parameters gsl_error_tol real This parameter controls the admissible error of the GSL integrator. Reduce it if NEST complains about numerical instabilities.

SpikeEvent