**Name:**

aeif_psc_delta - Current-based adaptive exponential integrate-and-fire

neuron model according to Brette and Gerstner (2005) with delta synapse.

**Description:**

aeif_psc_delta is the adaptive exponential integrate and fire neuron

according to Brette and Gerstner (2005), with post-synaptic 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:

C dV/dt= -g_L(V-E_L)+g_L*Delta_T*exp((V-V_T)/Delta_T)+I(t)+I_e

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.

**Parameters:**

C_m double - Capacity of the membrane in pF

t_ref double - Duration of refractory period in ms.

V_reset double - Reset value for V_m after a spike. In mV.

E_L double - Leak reversal potential in mV.

g_L double - Leak conductance in nS.

I_e double - Constant external input current in pA.

Spike adaptation parameters:

a double - Subthreshold adaptation in nS.

b double - Spike-triggered adaptation in pA.

Delta_T double - Slope factor in mV

tau_w double - Adaptation time constant in ms

V_th double - Spike initiation threshold in mV

V_peak double - Spike detection threshold in mV.

Integration parameters

gsl_error_tol double - This parameter controls the admissible error of the

GSL integrator. Reduce it if NEST complains about

numerical instabilities.

**Require:**

HAVE_GSL

**Receives:**

SpikeEvent, CurrentEvent, DataLoggingRequest

**Sends:**

SpikeEvent

**References:**

Brette R and Gerstner W (2005) Adaptive Exponential

Integrate-and-Fire Model as an Effective Description of

Neuronal Activity. J Neurophysiol 94:3637-3642

**Author:**

Mikkel Elle LepperÃ¸d adapted from aeif_psc_exp and iaf_psc_delta

**SeeAlso:**

**Source:**

/home/graber/work-nest/nest-git/nest-simulator/models/aeif_psc_delta.h