iaf_psc_alpha – Leaky integrate-and-fire neuron model
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Description
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``iaf_psc_alpha`` is an implementation of a leaky integrate-and-fire model
with alpha-function shaped synaptic currents. Thus, synaptic currents
and the resulting postsynaptic potentials have a finite rise time.
The threshold crossing is followed by an absolute refractory period
during which the membrane potential is clamped to the resting potential.
The linear subthreshold dynamics is integrated by the Exact
Integration scheme [1]_. 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
[1]_. A flow chart can be found in [2]_.
Critical tests for the formulation of the neuron model are the
comparisons of simulation results for different computation step
sizes and the testsuite contains a number of such tests.
The ``iaf_psc_alpha`` is the standard model used to check the consistency
of the nest simulation kernel because it is at the same time complex
enough to exhibit non-trivial dynamics and simple enough compute
relevant measures analytically.
.. 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_alpha 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 <../model_details/IAF_neurons_singularity.ipynb>`_ notebook.
See also [3]_.
Parameters
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The following parameters can be set in the status dictionary.
=========== ====== ==========================================================
V_m mV Membrane potential
E_L mV Resting 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_ex ms Rise time of the excitatory synaptic alpha function
tau_syn_in ms Rise time of the inhibitory synaptic alpha function
I_e pA Constant input current
V_min mV Absolute lower value for the membrane potenial
=========== ====== ==========================================================
References
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.. [1] 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
.. [2] 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
.. [3] Morrison A, Straube S, Plesser H E, Diesmann M (2006). Exact
subthreshold integration with continuous spike times in discrete time
neural network simulations. Neural Computation, in press
DOI: https://doi.org/10.1162/neco.2007.19.1.47
Sends
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SpikeEvent
Receives
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SpikeEvent, CurrentEvent, DataLoggingRequest
See also
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:doc:`Neuron `, :doc:`Integrate-And-Fire `, :doc:`Current-Based `