iaf_psc_exp

iaf_psc_exp - Leaky integrate-and-fire neuron model with exponential PSCs

Description

iaf_psc_exp is an implementation of a leaky integrate-and-fire model with exponential-kernel postsynaptic currents (PSCs) according to [1]. Thus, postsynaptic currents have an infinitely short rise time.

The threshold crossing is followed by an absolute refractory period (t_ref) during which the membrane potential is clamped to the resting potential and spiking is prohibited.

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

See also

iaf_cond_exp

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

ms

2ms

Duration of refractory period

E_L

mV

-70mV

Resting potential

V_reset

mV

-70mV

Reset value of the membrane potential

V_th

mV

-55mV

Spike threshold potential

I_e

pA

0pA

constant external input current

State variables

Name

Physical unit

Default value

Description

r

integer

0

Counts number of tick during the refractory period

V_m

mV

E_L

Membrane potential

Equations

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

Source code

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

Characterisation

Synaptic response

iaf_psc_exp_nestml

f-I curve

iaf_psc_exp_nestml