**Name:**

aeif_cond_exp - Conductance based exponential integrate-and-fire neuron

model according to Brette and Gerstner (2005).

**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.

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)-g_e(t)(V-E_e)

-g_i(t)(V-E_i)-w +I_e

and

tau_w * dw/dt= a(V-E_L) -W

Note that the spike detection threshold V_peak is automatically set to

V_th+10 mV to avoid numerical instabilites that may result from

setting V_peak too high.

**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_t double - Spike initiation threshold in mV

V_peak double - Spike detection threshold in mV.

Synaptic parameters

E_ex double - Excitatory reversal potential in mV.

tau_syn_ex double - Rise time of excitatory synaptic conductance in ms (exp

function).

E_in double - Inhibitory reversal potential in mV.

tau_syn_in double - Rise time of the inhibitory synaptic conductance in ms

(exp function).

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:**

Adapted from aeif_cond_alpha by Lyle Muller; full revision by Tanguy

Fardet on December 2016

**SeeAlso:**

**Source:**

/home/nest/work/nest-2.14.0/models/aeif_cond_exp.h