iaf_psc_exp

iaf_psc_exp - Leaky integrate-and-fire neuron model

Description

iaf_psc_exp is an implementation of a leaky integrate-and-fire model with exponentially decaying synaptic currents according to [1]. Thus, postsynaptic currents have an infinitely short rise time.

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

The general framework for the consistent formulation of systems with neuron like dynamics interacting by point events is described in [1]. A flow chart can be found in [2].

Critical tests for the formulation of the neuron model are the comparisons of simulation results for different computation step sizes.

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_psc_delta, iaf_psc_alpha, 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

refr_T

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

V_m

mV

E_L

Membrane potential

refr_t

ms

0ms

Refractory period timer

is_refractory

boolean

false

I_syn_exc

pA

0pA

I_syn_inh

pA

0pA

Equations

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

Source code

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

Characterisation

Synaptic response

iaf_psc_exp_neuron

f-I curve

iaf_psc_exp_neuron