iaf_psc_delta_ps – Current-based leaky integrate-and-fire neuron model with delta-shaped postsynaptic currents - precise spike timing version
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Description
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``iaf_psc_delta_ps`` is an implementation of a leaky integrate-and-fire model
where the potential jumps on each spike arrival.
The threshold crossing is followed by an absolute refractory period
during which the membrane potential is clamped to the resting
potential.
Spikes arriving while the neuron is refractory, are discarded by
default. If the property "refractory_input" is set to true, such
spikes are added to the membrane potential at the end of the
refractory period, dampened according to the interval between
arrival and end of refractoriness.
The linear subthreshold dynamics is integrated by the Exact
Integration scheme [1]_. The neuron dynamics are solved exactly in
time. Incoming and outgoing spike times are handled precisely [3]_.
An additional state variable and the corresponding differential
equation represents a piecewise constant external current.
Spikes can occur either on receipt of an excitatory input spike, or
be caused by a depolarizing input current. Spikes evoked by
incoming spikes, will occur precisely at the time of spike arrival,
since incoming spikes are modeled as instantaneous potential
jumps. Times of spikes caused by current input are determined
exactly by solving the membrane potential equation. Note that, in
contrast to the neuron models discussed in [3]_ [4]_, this model has so
simple dynamics that no interpolation or iterative spike location
technique is required at all.
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_delta_ps`` 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.
Please note that this node is capable of sending precise spike times
to target nodes (on-grid spike time plus offset).
The ``af_psc_delta_ps`` neuron accepts connections transmitting
``CurrentEvents``. These events transmit stepwise-constant currents which
can only change at on-grid times.
For details about exact subthreshold integration, please see
:doc:`../neurons/exact-integration`.
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 Capacitance of the membrane
tau_m ms Membrane time constant
t_ref ms Duration of refractory period
V_th ms Spike threshold
V_reset mV Reset potential of the membrane
I_e pA Constant input current
V_min mV Absolute lower value for the membrane potential
refractory_input (bool) If true, keep input during refractory period (default: false)
================= ====== ==============================================================
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.
.. [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.
.. [3] Morrison A, Straube S, Plesser H E, & Diesmann M (2006) Exact
Subthreshold Integration with Continuous Spike Times in Discrete Time Neural
Network Simulations. To appear in Neural Computation.
.. [4] Hanuschkin A, Kunkel S, Helias M, Morrison A & Diesmann M (2010)
A general and efficient method for incorporating exact spike times in
globally time-driven simulations Front Neuroinformatics, 4:113
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 `, :doc:`Precise `
Examples using this model
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.. listexamples:: iaf_psc_delta_ps