aeif_psc_delta – Current-based adaptive exponential integrate-and-fire neuron model with delta synapse

Description

aeif_psc_delta is the adaptive exponential integrate and fire neuron according to [1], with postsynaptic currents in the form of delta spikes.

This implementation uses the embedded 5th order Runge-Kutta solver with adaptive stepsize to integrate the differential equation.

The membrane potential is given by the following differential equation:

\[C_m \frac{dV}{dt} = -g_L(V-E_L) + g_L\Delta_T \exp\left(\frac{V-V_{th}}{\Delta_T}\right) + I(t)- w + I_e\]

and

\[\tau_w dw/dt= a(V-E_L) -w\]

\[I(t) = J \sum_k \delta(t - t^k).\]

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.

Note

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 models). The time constants are supplied by an array, tau_syn. 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

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

[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

See also

Neuron, Adaptive Threshold, Integrate-And-Fire, Current-Based