# iaf_psc_delta_ps – Current-based leaky integrate-and-fire neuron model with delta-shaped postsynaptic currents - precise spike timing version¶

## Description¶

`iaf_psc_delta_ps`

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 “refractory_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 linear subthreshold dynamics is integrated by the Exact Integration scheme 1. The neuron dynamics are solved exactly in time. Incoming and outgoing spike times are handled precisely 3.

An additional state variable and the corresponding differential equation represents a piecewise constant external current.

Spikes can occur either on receipt of an excitatory input spike, or be caused by a depolarizing input current. Spikes evoked by incoming spikes, will occur precisely at the time of spike arrival, since incoming spikes are modeled as instantaneous potential jumps. Times of spikes caused by current input are determined exactly by solving the membrane potential equation. Note that, in contrast to the neuron models discussed in 3 4, this model has so simple dynamics that no interpolation or iterative spike location technique is required at all.

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 and the testsuite contains a number of such tests.

The `iaf_psc_delta_ps`

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.

Please note that this node is capable of sending precise spike times to target nodes (on-grid spike time plus offset).

The `af_psc_delta_ps`

neuron accepts connections transmitting
`CurrentEvents`

. These events transmit stepwise-constant currents which
can only change at on-grid times.

For details about exact subthreshold integration, please see Integrating neural models using exact integration.

## Parameters¶

The following parameters can be set in the status dictionary.

V_m |
mV |
Membrane potential |

E_L |
mV |
Resting membrane potential |

C_m |
pF |
Capacitance of the membrane |

tau_m |
ms |
Membrane time constant |

t_ref |
ms |
Duration of refractory period |

V_th |
ms |
Spike threshold |

V_reset |
mV |
Reset potential of the membrane |

I_e |
pA |
Constant input current |

V_min |
mV |
Absolute lower value for the membrane potential |

refractory_input |
(bool) |
If true, keep input during refractory period (default: false) |

## References¶

- 1(1,2)
Rotter S & Diesmann M (1999) Exact simulation of time-invariant linear systems with applications to neuronal modeling. Biologial Cybernetics 81:381-402.

- 2
Diesmann M, Gewaltig M-O, Rotter S, & Aertsen A (2001) State space analysis of synchronous spiking in cortical neural networks. Neurocomputing 38-40:565-571.

- 3(1,2)
Morrison A, Straube S, Plesser H E, & Diesmann M (2006) Exact Subthreshold Integration with Continuous Spike Times in Discrete Time Neural Network Simulations. To appear in Neural Computation.

- 4
Hanuschkin A, Kunkel S, Helias M, Morrison A & Diesmann M (2010) A general and efficient method for incorporating exact spike times in globally time-driven simulations Front Neuroinformatics, 4:113

## Sends¶

SpikeEvent

## Receives¶

SpikeEvent, CurrentEvent, DataLoggingRequest