iaf_psc_exp_htum – Leaky integrate-and-fire model with separate relative and absolute refractory period
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Description
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``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 Integration Singularity notebook <../model_details/IAF_Integration_Singularity.ipynb>`_.
See also [4]_.
Parameters
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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
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.. [1] 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] 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
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SpikeEvent
Receives
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SpikeEvent, CurrentEvent, DataLoggingRequest
Examples using this model
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.. listexamples:: iaf_psc_exp_htum