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This is A PREVIEW for NEST 3.0 and NOT an OFFICIAL RELEASE! Some functionality may not be available and information may be incomplete!

iaf_psc_exp_htum – Leaky integrate-and-fire model with separate relative and absolute refractory period

Description

iaf_psc_exp_htum is an implementation of a leaky integrate-and-fire model with exponential shaped postsynaptic currents (PSCs) according to 1. The postsynaptic currents have an infinitely short rise time. In particular, this model allows setting an absolute and relative refractory time separately, as required by 1.

The threshold crossing is followed by an absolute refractory period (t_ref_abs) during which the membrane potential is clamped to the resting potential. During the total refractory period (t_ref_tot), the membrane potential evolves, but the neuron will not emit a spike, even if the membrane potential reaches threshold. The total refractory time must be larger or equal to the absolute refractory time. If equal, the refractoriness of the model if equivalent to the other models of NEST.

The linear subthreshold dynamics is integrated by the Exact Integration scheme 2. The neuron dynamics is solved on the time grid given by the computation step size. Incoming as well as emitted spikes are forced to that grid.

An additional state variable and the corresponding differential equation represents a piecewise constant external current.

The general framework for the consistent formulation of systems with neuron like dynamics interacting by point events is described in 2. A flow chart can be found in 3.

Note

The present implementation uses individual variables for the components of the state vector and the non-zero matrix elements of the propagator. Because the propagator is a lower triangular matrix, no full matrix multiplication needs to be carried out and the computation can be done “in place”, i.e. no temporary state vector object is required.

The template support of recent C++ compilers enables a more succinct formulation without loss of runtime performance already at minimal optimization levels. A future version of iaf_psc_exp_htum will probably address the problem of efficient usage of appropriate vector and matrix objects.

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.

E_L

mV

Resting membrane potenial

C_m

pF

Capacity of the membrane

tau_m

ms

Membrane time constant

tau_syn_ex

ms

Time constant of postsynaptic excitatory currents

tau_syn_in

ms

Time constant of postsynaptic inhibitory currents

t_ref_abs

ms

Duration of absolute refractory period (V_m = V_reset)

t_ref_tot

ms

Duration of total refractory period (no spiking)

V_m

mV

Membrane potential

V_th

mV

Spike threshold

V_reset

mV

Reset membrane potential after a spike

I_e

pA

Constant input current

t_spike

ms

Point in time of last spike

References

1(1,2)

Tsodyks M, Uziel A, Markram H (2000). Synchrony generation in recurrent networks with frequency-dependent synapses. The Journal of Neuroscience, 20,RC50:1-5. URL: https://infoscience.epfl.ch/record/183402

2(1,2)

Hill, A. V. (1936). Excitation and accommodation in nerve. Proceedings of the Royal Society of London. Series B-Biological Sciences, 119(814), 305-355. DOI: https://doi.org/10.1098/rspb.1936.0012

3

Rotter S, Diesmann M (1999). Exact simulation of time-invariant linear systems with applications to neuronal modeling. Biologial Cybernetics 81:381-402. DOI: https://doi.org/10.1007/s004220050570

4

Diesmann M, Gewaltig M-O, Rotter S, & Aertsen A (2001). State space analysis of synchronous spiking in cortical neural networks. Neurocomputing 38-40:565-571. DOI: https://doi.org/10.1016/S0925-2312(01)00409-X

Sends

SpikeEvent

Receives

SpikeEvent, CurrentEvent, DataLoggingRequest