aeif_psc_delta - Current-based adaptive exponential integrate-and-fire
neuron model according to Brette and Gerstner (2005) with delta synapse.
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:
@f[ 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 @f]
and
@f[ \tau_w * dw/dt= a(V-E_L) -W @f]
@f[ I(t) = J \sum_k \delta(t - t^k). @f]
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.
The following parameters can be set in the status dictionary.
\verbatim embed:rst
======== ======= =======================================
**Dynamic state variables**
--------------------------------------------------------
V_m mV Membrane potential
w pA Spike-adaptation current
======== ======= =======================================
======== ======= =======================================
**Membrane Parameters**
--------------------------------------------------------
C_m pF Capacity of the membrane
t_ref ms Duration of refractory period
V_reset mV Reset value for V_m after a spike
E_L mV Leak reversal potential
g_L nS Leak conductance
I_e pA Constant external input current
======== ======= =======================================
======== ======= ==================================
**Spike adaptation parameters**
---------------------------------------------------
a ns Subthreshold adaptation
b pA Spike-triggered adaptation
tau_w ms Adaptation time constant
Delta_T mV Slope factor
tau_w ms Adaptation time constant
V_th mV Spike initiation threshold
V_peak mV Spike detection threshold
======== ======= ==================================
============= ======= =========================================================
**Integration parameters**
-------------------------------------------------------------------------------
gsl_error_tol real This parameter controls the admissible error of the
GSL integrator. Reduce it if NEST complains about
numerical instabilities.
============= ======= =========================================================
\endverbatim
SpikeEvent, CurrentEvent, DataLoggingRequest
SpikeEvent
\verbatim embed:rst
.. [1] Brette R and Gerstner W (2005). Adaptive Exponential
Integrate-and-Fire Model as an Effective Description of Neuronal
Activity. J Neurophysiol 94:3637-3642.
DOI: https://doi.org/10.1152/jn.00686.2005
\endverbatim
Mikkel Elle Lepperød adapted from aeif_psc_exp and iaf_psc_delta
/var/www/debian/nest/nest-simulator-2.18.0/models/aeif_psc_delta.h