iaf_psc_delta_ps – Current-based leaky integrate-and-fire neuron model with delta-shaped postsynaptic currents - precise spike timing version
=============================================================================================================================================

Description
+++++++++++

``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
++++++++++

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
++++++++++

.. [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
+++++

SpikeEvent

Receives
++++++++

SpikeEvent, CurrentEvent, DataLoggingRequest

See also
++++++++
:doc:`Neuron <index_neuron>`, :doc:`Integrate-And-Fire <index_integrate-and-fire>`, :doc:`Current-Based <index_current-based>`, :doc:`Precise <index_precise>`

Examples using this model
+++++++++++++++++++++++++

.. listexamples:: iaf_psc_delta_ps