# iaf_psc_delta

iaf_psc_delta - Current-based leaky integrate-and-fire neuron model with delta-kernel post-synaptic currents

## Description

iaf_psc_delta is an implementation of a leaky integrate-and-fire model where the potential jumps on each spike arrival.

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

Spikes arriving while the neuron is refractory, are discarded by
default. If the property `with_refr_input`

is set to true, such
spikes are added to the membrane potential at the end of the
refractory period, dampened according to the interval between
arrival and end of refractoriness.

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. sli/testsuite/nest contains a number of such tests.

The iaf_psc_delta is the standard model used to check the consistency of the nest simulation kernel because it is at the same time complex enough to exhibit non-trivial dynamics and simple enough compute relevant measures analytically.

## References

## See also

iaf_psc_alpha, iaf_psc_exp

## Parameters

Name |
Physical unit |
Default value |
Description |
---|---|---|---|

tau_m |
ms |
10ms |
Membrane time constant |

C_m |
pF |
250pF |
Capacity of the membrane |

refr_T |
ms |
2ms |
Duration of refractory period |

tau_syn |
ms |
2ms |
Time constant of synaptic current |

E_L |
mV |
-70mV |
Resting membrane potential |

V_reset |
mV |
-70mV |
Reset potential of the membrane |

V_th |
mV |
-55mV |
Spike threshold |

V_min |
mV |
-inf * 1mV |
Absolute lower value for the membrane 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 |

## Equations

## Source code

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