iaf_psc_alpha – Leaky integrate-and-fire neuron model ===================================================== Description +++++++++++ ``iaf_psc_alpha`` is an implementation of a leaky integrate-and-fire model with alpha-function shaped synaptic currents. Thus, synaptic currents and the resulting postsynaptic potentials have a finite rise time. The threshold crossing is followed by an absolute refractory period during which the membrane potential is clamped to the resting potential. The linear subthreshold dynamics is integrated by the Exact Integration scheme [1]_. The neuron dynamics is solved on the time grid given by the computation step size. Incoming as well as emitted spikes are forced to that grid. An additional state variable and the corresponding differential equation represents a piecewise constant external current. 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_alpha`` 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. .. note:: The present implementation uses individual variables for the components of the state vector and the non-zero matrix elements of the propagator. Because the propagator is a lower triangular matrix, no full matrix multiplication needs to be carried out and the computation can be done "in place", i.e. no temporary state vector object is required. The template support of recent C++ compilers enables a more succinct formulation without loss of runtime performance already at minimal optimization levels. A future version of iaf_psc_alpha will probably address the problem of efficient usage of appropriate vector and matrix objects. .. 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. See also [3]_. 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 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 alpha function tau_syn_in ms Rise time of the inhibitory synaptic alpha function I_e pA Constant input current V_min mV Absolute lower value for the membrane potenial =========== ====== ========================================================== References ++++++++++ .. [1] Rotter S, Diesmann M (1999). Exact simulation of time-invariant linear systems with applications to neuronal modeling. Biologial Cybernetics 81:381-402. DOI: https://doi.org/10.1007/s004220050570 .. [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. DOI: https://doi.org/10.1016/S0925-2312(01)00409-X .. [3] Morrison A, Straube S, Plesser H E, Diesmann M (2006). Exact subthreshold integration with continuous spike times in discrete time neural network simulations. Neural Computation, in press DOI: https://doi.org/10.1162/neco.2007.19.1.47 Sends +++++ SpikeEvent Receives ++++++++ SpikeEvent, CurrentEvent, DataLoggingRequest See also ++++++++ :doc:`Neuron `, :doc:`Integrate-And-Fire `, :doc:`Current-Based `