aeif_cond_beta – Conductance-based adaptive exponential integrate-and-fire neuron model¶
Description¶
aeif_cond_beta
is a conductance-based adaptive exponential
integrate-and-fire neuron model according to [1] with
multiple synaptic rise time and decay time constants, and synaptic conductance
modeled by a beta function.
This implementation uses the 5th order Runge-Kutta solver with adaptive step size to integrate the differential equation.
It allows an arbitrary number of synaptic rise time and decay time constants. Synaptic conductance is modeled by a beta function, as described in [2].
The membrane potential is given by the following differential equation:
where:
the synapse i is excitatory or inhibitory depending on the value of \(E_{rev,i}\) and the differential equation for the spike-adaptation current w is
When the neuron fires a spike, the adaptation current w <- w + b.
Note
As mentioned in the Differences between NEST GPU and NEST,
all the aeif neuron models in NEST GPU are multisynapse models.
The number of receptor ports must be specified at neuron creation (default value is 1) and
the receptor index starts from 0 (and not from 1 as in NEST multisynapse models).
The time constants are supplied by by two arrays, tau_rise
and tau_decay
for
the synaptic rise time and decay time, respectively. The synaptic
reversal potentials are supplied by the array E_rev
. Port numbers
are automatically assigned in the range 0 to n_receptors-1
.
During connection, the ports are selected with the synapse property receptor
.
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 |
||
V_th |
mV |
Spike initiation threshold |
Delta_T |
mV |
Slope factor |
g_L |
nS |
Leak conductance |
E_L |
mV |
Leak reversal potential |
C_m |
pF |
Capacity of the membrane |
I_e |
pA |
Constant external input current |
V_peak |
mV |
Spike detection threshold |
V_reset |
mV |
Reset value for V_m after a spike |
t_ref |
ms |
Duration of refractory period |
den_delay |
ms |
Dendritic delay |
Spike adaptation parameters |
||
a |
ns |
Subthreshold adaptation |
b |
pA |
Spike-triggered adaptation |
tau_w |
ms |
Adaptation time constant |
Synaptic parameters |
||
E_rev |
list of mV |
Reversal potential |
tau_rise |
list of ms |
Rise time constant of synaptic conductance |
tau_decay |
list of ms |
Decay time constant of synaptic conductance |
Integration parameters |
||
h0_rel |
real |
Starting step in ODE integration relative to time resolution |
h_min_rel |
real |
Minimum step in ODE integration relative to time resolution |
References¶
See also¶
Neuron, Adaptive Threshold, Integrate-And-Fire, Conductance-Based