# iaf_psc_alpha_ps – Current-based leaky integrate-and-fire neuron with alpha-shaped postsynaptic currents using regula falsi method for approximation of threshold crossing¶

## Description¶

New in version 2.18.

`iaf_psc_alpha_ps`

is the “canonical” implementation of the leaky
integrate-and-fire model neuron with alpha-shaped postsynaptic
currents in the sense of 1. This is the most exact implementation
available.

PSCs are normalized to an amplitude of 1pA.

The precise implementation handles neuronal dynamics in a locally event-based manner with in coarse time grid defined by the minimum delay in the network, see 1. Incoming spikes are applied at the precise moment of their arrival, while the precise time of outgoing spikes is determined by a Regula Falsi method to approximate the timing of a threshold crossing 1 3. Return from refractoriness occurs precisely at spike time plus refractory period.

This implementation is more complex than the plain iaf_psc_alpha neuron, but achieves much higher precision. In particular, it does not suffer any binning of spike times to grid points. Depending on your application, the canonical application may provide superior overall performance given an accuracy goal; see 1 for details. Subthreshold dynamics are integrated using exact integration between events 2.

This model transmits precise spike times to target nodes (on-grid spike time and offset). If this node is connected to a spike_recorder, the property “precise_times” of the spike_recorder has to be set to true in order to record the offsets in addition to the on-grid spike times.

The iaf_psc_alpha_ps neuron accepts connections transmitting CurrentEvents. These events transmit stepwise-constant currents which can only change at on-grid times.

Note

If tau_m is very close to tau_syn_ex or tau_syn_in, the model will numerically behave as if tau_m is equal to tau_syn_ex or tau_syn_in, respectively, to avoid numerical instabilities.

For implementation details see the IAF_neurons_singularity notebook.

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 |

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

C_m |
pF |
Capacity of the membrane |

tau_m |
ms |
Membrane time constant |

t_ref |
ms |
Duration of refractory period |

V_th |
mV |
Spike threshold |

V_reset |
mV |
Reset potential of the membrane |

tau_syn_ex |
ms |
Rise time of the excitatory synaptic function |

tau_syn_in |
ms |
Rise time of the inhibitory synaptic function |

I_e |
pA |
Constant external input current |

## References¶

- 1(1,2,3,4)
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.

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

- 3
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