# 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.

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.

## 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 |

## 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