**Name:**

iaf_psc_exp_ps - Leaky integrate-and-fire neuron

with exponential postsynaptic currents; canoncial implementation;

bisectioning 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 bisectioning method to approximate the timing of a threshold

crossing [1,2]. 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 bisectioning 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 bisectioning 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 double - Resting membrane potential in mV.

C_m double - Capacitance of the membrane in pF.

tau_m double - Membrane time constant in ms.

tau_syn_ex double - Excitatory synaptic time constant in ms.

tau_syn_in double - Inhibitory synaptic time constant in ms.

t_ref double - Duration of refractory period in ms.

V_th double - Spike threshold in mV.

I_e double - Constant input current in pA.

V_min double - Absolute lower value for the membrane potential in mV.

V_reset double - Reset value for the membrane potential in mV.

**Receives:**

SpikeEvent, CurrentEvent, DataLoggingRequest

**Sends:**

SpikeEvent

**Remarks:**

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 details, please see IAF_Neruons_Singularity.ipynb in the

NEST source code (docs/model_details).

**References:**

[1] 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] 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

**Author:**

Kunkel

**SeeAlso:**

**Source:**

/home/graber/work-nest/nest-git/nest-simulator/precise/iaf_psc_exp_ps.h