# iaf_psc_alpha_canon – Current-based leaky integrate-and-fire neuron with alpha-shaped postsynaptic currents - canonical implementation of precise spike timing version¶

## Description¶

Note

This model is deprecated and will be removed in NEST 3.
Please use `iaf_psc_alpha_ps`

instead.

iaf_psc_alpha_canon is the “canonical” implementatoin 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 canonical 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 interpolation once a threshold crossing has been detected. Return from refractoriness occurs precisly 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.

Note

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

A further improvement of precise simulation is implemented in iaf_psc_exp_ps based on 3.

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.

## 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 |
ms |
Rise time of the synaptic alpha function |

I_e |
pA |
Constant external input current |

Interpol_Order |
(int) |
Interpolation order for spike time: 0-none, 1-linear, 2-quadratic, 3-cubic |

## Remarks¶

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_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.

## References¶

- 1(1,2,3)
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