iaf_psc_exp_htum

iaf_psc_exp_htum - Leaky integrate-and-fire model with separate relative and absolute refractory period

Description

iaf_psc_exp_htum is an implementation of a leaky integrate-and-fire model with exponential-kernel postsynaptic currents (PSCs) according to [1]. The postsynaptic currents have an infinitely short rise time. In particular, this model allows setting an absolute and relative refractory time separately, as required by [1].

The threshold crossing is followed by an absolute refractory period (t_ref_abs) during which the membrane potential is clamped to the resting potential. During the total refractory period (t_ref_tot), the membrane potential evolves, but the neuron will not emit a spike, even if the membrane potential reaches threshold. The total refractory time must be larger or equal to the absolute refractory time. If equal, the refractoriness of the model if equivalent to the other models of NEST.

Note

This neuron model can only be used in combination with a fixed simulation resolution (timestep size).

Note

If tau_m is very close to tau_syn_exc or tau_syn_inh, numerical problems may arise due to singularities in the propagator matrics. If this is the case, replace equal-valued parameters by a single parameter.

For details, please see IAF_neurons_singularity.ipynb in the NEST source code (docs/model_details).

References

Parameters

Name

Physical unit

Default value

Description

C_m

pF

250pF

Capacitance of the membrane

tau_m

ms

10ms

Membrane time constant

tau_syn_inh

ms

2ms

Time constant of inhibitory synaptic current

tau_syn_exc

ms

2ms

Time constant of excitatory synaptic current

t_ref_abs

ms

2ms

Absolute refractory period

t_ref_tot

ms

2ms

total refractory period, if t_ref_abs == t_ref_tot iaf_psc_exp_htum equivalent to iaf_psc_exp

E_L

mV

-70mV

Resting potential

V_reset

mV

-70.0mV - E_L

Reset value of the membrane potentia. lRELATIVE TO RESTING POTENTIAL(!) I.e. the real threshold is (V_reset + E_L).

V_th

mV

-55.0mV - E_L

Threshold, RELATIVE TO RESTING POTENTIAL(!) I.e. the real threshold is (E_L + V_th)

I_e

pA

0pA

constant external input current

State variables

Name

Physical unit

Default value

Description

r_tot

integer

0

r_abs

integer

0

V_m

mV

0.0mV

Membrane potential

Equations

\[\frac{ dV_{m} } { dt }= \frac{ -V_{m} } { \tau_{m} } + \frac 1 { C_{m} } \left( { (I_{syn} + I_{e} + I_{stim}) } \right)\]

Source code

The model source code can be found in the NESTML models repository here: iaf_psc_exp_htum.

Characterisation