iaf_psc_exp_ps – Current-based leaky integrate-and-fire neuron with exponential-shaped postsynaptic currents using regula falsi method for approximation of threshold crossing
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Description
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``iaf_psc_exp_ps`` is the "canonical" implementation of the leaky
integrate-and-fire model neuron with exponential postsynaptic currents
that uses the regula falsi method to approximate the timing of a threshold
crossing. This is the most exact implementation available.

The canonical implementation handles neuronal dynamics in a locally
event-based manner with in coarse time grid defined by the minimum
delay in the network, see [1]_ [2]_. Incoming spikes are applied at the
precise moment of their arrival, while the precise time of outgoing
spikes is determined by regula falsi once a threshold crossing has
been detected. Return from refractoriness occurs precisely at spike
time plus refractory period.

This implementation is more complex than the plain iaf_psc_exp
neuron, but achieves much higher precision. In particular, it does not
suffer any binning of spike times to grid points. Depending on your
application, the canonical application with regula falsi may provide
superior overall performance given an accuracy goal; see [1]_ [2]_ for
details. Subthreshold dynamics are integrated using exact integration
between events [3]_.

Please note that this node is capable of sending precise spike times
to target nodes (on-grid spike time and offset).

The iaf_psc_delta_ps neuron accepts connections transmitting
CurrentEvents. These events transmit stepwise-constant currents which
can only change at on-grid times.

.. 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>`_.

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.

==========  =====  ==========================================================
E_L         mV     Resting membrane potential
C_m         pF     Capacitance of the membrane
tau_m       ms     Membrane time constant
tau_syn_ex  ms     Excitatory synaptic time constant
tau_syn_in  ms     Inhibitory synaptic time constant
t_ref       ms     Duration of refractory period
V_th        mV     Spike threshold
I_e         pA     Constant input current
V_min       mV     Absolute lower value for the membrane potential
V_reset     mV     Reset value for the membrane potential
==========  =====  ==========================================================

References
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.. [1] Morrison A, Straube S, Plesser HE & Diesmann M (2007) Exact subthreshold
       integration with continuous spike times in discrete time neural network
       simulations. Neural Comput 19, 47-79
.. [2] Hanuschkin A, Kunkel S, Helias M, Morrison A and Diesmann M (2010) A
       general and efficient method for incorporating precise spike times in
       globally timedriven simulations. Front Neuroinform 4:113
.. [3] Rotter S & Diesmann M (1999) Exact simulation of time-invariant linear
       systems with applications to neuronal modeling. Biol Cybern 81:381-402

Sends
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SpikeEvent

Receives
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SpikeEvent, CurrentEvent, DataLoggingRequest

See also
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: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
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.. listexamples:: iaf_psc_exp_ps