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

## Description¶

iaf_psc_exp_ps is the “canonical” implementation of the leaky integrate-and-fire model neuron with exponential postsynaptic currents that uses the regula falsi method to approximate the timing of a threshold crossing. This is the most exact implementation available.

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 2. Incoming spikes are applied at the precise moment of their arrival, while the precise time of outgoing spikes is determined by regula falsi once a threshold crossing has been detected. Return from refractoriness occurs precisely at spike time plus refractory period.

This implementation is more complex than the plain iaf_psc_exp 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 with regula falsi may provide superior overall performance given an accuracy goal; see 1 2 for details. Subthreshold dynamics are integrated using exact integration between events 3.

## Parameters¶

The following parameters can be set in the status dictionary.

E_L |
mV |
Resting membrane potential |

C_m |
pF |
Capacitance of the membrane |

tau_m |
ms |
Membrane time constant |

tau_syn_ex |
ms |
Excitatory synaptic time constant |

tau_syn_in |
ms |
Inhibitory synaptic time constant |

t_ref |
ms |
Duration of refractory period |

V_th |
mV |
Spike threshold |

I_e |
pA |
Constant input current |

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

V_reset |
mV |
Reset value for the membrane potential |

## Remarks¶

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

The iaf_psc_delta_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.

## References¶

- 1(1,2)
Morrison A, Straube S, Plesser HE & Diesmann M (2007) Exact subthreshold integration with continuous spike times in discrete time neural network simulations. Neural Comput 19, 47-79

- 2(1,2)
Hanuschkin A, Kunkel S, Helias M, Morrison A and Diesmann M (2010) A general and efficient method for incorporating precise spike times in globally timedriven simulations. Front Neuroinform 4:113

- 3
Rotter S & Diesmann M (1999) Exact simulation of time-invariant linear systems with applications to neuronal modeling. Biol Cybern 81:381-402

## Sends¶

SpikeEvent

## Receives¶

SpikeEvent, CurrentEvent, DataLoggingRequest