aeif_cond_alpha -   Conductance based exponential integrate-and-fire neuron  
model according to Brette and Gerstner (2005).
aeif_cond_alpha is the adaptive exponential integrate and fire neuron according
to Brette and Gerstner (2005).
Synaptic conductances are modelled as alpha-functions.

This implementation uses the embedded 4th order Runge-Kutta-Fehlberg solver with
adaptive step size 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


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

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.

Synaptic parameters
E_ex double - Excitatory reversal potential in mV.
tau_syn_ex double - Rise time of excitatory synaptic conductance in ms (alpha
E_in double - Inhibitory reversal potential in mV.
tau_syn_in double - Rise time of the inhibitory synaptic conductance in ms
(alpha 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.

SpikeEvent, CurrentEvent, DataLoggingRequest  


Brette R and Gerstner W (2005) Adaptive Exponential  
Integrate-and-Fire Model as an Effective Description of Neuronal
Activity. J Neurophysiol 94:3637-3642

Marc-Oliver Gewaltig; full revision by Tanguy Fardet on December 2016  

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