iaf_psc_alpha_ps – Current-based leaky integrate-and-fire neuron with alpha-shaped postsynaptic currents using regula falsi method for approximation of threshold crossing ========================================================================================================================================================================== Description +++++++++++ .. versionadded:: 2.18 ``iaf_psc_alpha_ps`` is the "canonical" implementation of the leaky integrate-and-fire model neuron with alpha-shaped postsynaptic currents in the sense of [1]_. This is the most exact implementation available. PSCs are normalized to an amplitude of 1pA. The precise 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 a Regula Falsi method to approximate the timing of a threshold crossing [1]_ [3]_. Return from refractoriness occurs precisely 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]_. This model transmits precise spike times to target nodes (on-grid spike time and offset). If this node is connected to a spike_recorder, the property "precise_times" of the spike_recorder has to be set to true in order to record the offsets in addition to the on-grid spike times. The iaf_psc_alpha_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_neurons_singularity <../model_details/IAF_neurons_singularity.ipynb>`_ notebook. 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 V_min mV Absolute lower value for the 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 function tau_syn_in ms Rise time of the inhibitory synaptic function I_e pA Constant external input current =========== ====== ========================================================== References ++++++++++ .. [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 81:381-402. .. [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 Sends +++++ SpikeEvent Receives ++++++++ SpikeEvent, CurrentEvent, DataLoggingRequest See also ++++++++ :doc:`Neuron `, :doc:`Integrate-And-Fire `, :doc:`Current-Based `, :doc:`Precise `