iaf_psc_alpha_canon - Leaky integrate-and-fire neuron  
with alpha-shape postsynaptic currents; canoncial implementation.
iaf_psc_alpha_canon is the "canonical" implementatoin of the leaky
integrate-and-fire model neuron with alpha-shaped postsynaptic
currents in the sense of [1]. This is the most exact implementation

PSCs are normalized to an amplitude of 1pA.

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]. Incoming spikes are applied at the
precise moment of their arrival, while the precise time of outgoing
spikes is determined by interpolation once a threshold crossing has
been detected. Return from refractoriness occurs precisly at spike
time plus refractory period.

This implementation is more complex than the plain iaf_psc_alpha
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 may provide superior overall
performance given an accuracy goal; see [1] for details. Subthreshold
dynamics are integrated using exact integration between events [2].

The following parameters can be set in the status dictionary.

V_m double - Membrane potential in mV
E_L double - Resting membrane potential in mV.
V_min double - Absolute lower value for the membrane potential.
C_m double - Capacity of the membrane in pF
tau_m double - Membrane time constant in ms.
t_ref double - Duration of refractory period in ms.
V_th double - Spike threshold in mV.
V_reset double - Reset potential of the membrane in mV.
tau_syn double - Rise time of the synaptic alpha function in ms.
I_e double - Constant external input current in pA.
Interpol_Order int - Interpolation order for spike time:
0-none, 1-linear, 2-quadratic, 3-cubic

SpikeEvent, CurrentEvent, DataLoggingRequest  


If tau_m is very close to tau_syn, the model will numerically behave as
if tau_m is equal to tau_syn, to avoid numerical instabilities.
For details, please see IAF_Neruons_Singularity.ipynb in
the NEST source code (docs/model_details).

[1] 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.
[2] Rotter S & Diesmann M (1999) Exact simulation of time-invariant linear
systems with applications to neuronal modeling. Biologial Cybernetics
[3] 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

Diesmann, Eppler, Morrison, Plesser, Straube  

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