**Name:**

aeif_cond_alpha_RK5 - Conductance based exponential integrate-and-fire

neuron model according to Brette and Gerstner (2005)

**Description:**

aeif_cond_alpha_RK5 is the adaptive exponential integrate and fire neuron

according to Brette and Gerstner (2005).

Synaptic conductances are modelled as alpha-functions.

This implementation uses a 5th order Runge-Kutta solver with adaptive stepsize

to integrate the differential equation (see Numerical Recipes 3rd Edition,

Press et al. 2007, Ch. 17.2).

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

**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.

Synaptic parameters:

E_ex double - Excitatory reversal potential in mV.

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

function).

E_in double - Inhibitory reversal potential in mV.

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

(alpha function).

Numerical integration parameters:

HMIN double - Minimal stepsize for numerical integration in ms

(default 0.001ms).

MAXERR double - Error estimate tolerance for adaptive stepsize control

(steps accepted if err<=MAXERR). In mV.

Note that the error refers to the difference between the

4th and 5th order RK terms. Default 1e-10 mV.

Authors: Stefan Bucher, Marc-Oliver Gewaltig.

**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

**SeeAlso:**

**Source:**

/home/graber/work-nest/nest-git/nest-simulator/models/aeif_cond_alpha_RK5.h