aeif_cond_alpha_multisynapse – Conductance based adaptive exponential integrate-and-fire neuron model ===================================================================================================== Description +++++++++++ ``aeif_cond_alpha_multisynapse`` is a conductance-based adaptive exponential integrate-and-fire neuron model according to Brette and Gerstner (2005) with multiple synaptic rise time and decay time constants, and synaptic conductance modeled by an alpha function. It allows an arbitrary number of synaptic time constants. Synaptic conductance is modeled by an alpha function, as described by A. Roth and M. C. W. van Rossum in Computational Modeling Methods for Neuroscientists, MIT Press 2013, Chapter 6. The time constants are supplied by an array, ``tau_syn``, and the pertaining synaptic reversal potentials are supplied by the array ``E_rev``. Port numbers are automatically assigned in the range from 1 to n_receptors. During connection, the ports are selected with the property ``receptor_type``. When connecting to conductance-based multisynapse models, all synaptic weights must be non-negative. The membrane potential is given by the following differential equation: .. math:: C dV/dt = -g_L(V-E_L) + g_L \cdot \Delta_T \cdot \exp((V-V_T)/\Delta_T) + I_{syn_{tot}}(V, t)- w + I_e where .. math:: I_{syn_{tot}}(V,t) = \sum_i g_i(t) (V - E_{rev,i}) , the synapse `i` is excitatory or inhibitory depending on the value of :math:`E_{rev,i}` and the differential equation for the spike-adaptation current `w` is .. math:: \tau_w \cdot dw/dt = a(V - E_L) - w When the neuron fires a spike, the adaptation current :math:`w <- w + b`. For implementation details see the `aeif_models_implementation <../model_details/aeif_models_implementation.ipynb>`_ notebook. Parameters ++++++++++ The following parameters can be set in the status dictionary. ======== ======= ======================================= **Dynamic state variables:** -------------------------------------------------------- V_m mV Membrane potential w pA Spike-adaptation current ======== ======= ======================================= ======== ======= ======================================= **Membrane Parameters** -------------------------------------------------------- C_m pF Capacity of the membrane t_ref ms Duration of refractory period V_reset mV Reset value for V_m after a spike E_L mV Leak reversal potential g_L nS Leak conductance I_e pA Constant external input current Delta_T mV Slope factor V_th mV Spike initiation threshold V_peak mV Spike detection threshold ======== ======= ======================================= ======== ======= ================================== **Spike adaptation parameters** --------------------------------------------------- a ns Subthreshold adaptation b pA Spike-triggered adaptation tau_w ms Adaptation time constant ======== ======= ================================== ======== ============= ======================================================== **Synaptic parameters** ------------------------------------------------------------------------------- E_rev list of mV Reversal potential tau_syn list of ms Time constant of synaptic conductance ======== ============= ======================================================== ============= ======= ========================================================= **Integration parameters** ------------------------------------------------------------------------------- gsl_error_tol real This parameter controls the admissible error of the GSL integrator. Reduce it if NEST complains about numerical instabilities. ============= ======= ========================================================= Sends +++++ SpikeEvent Receives ++++++++ SpikeEvent, CurrentEvent, DataLoggingRequest See also ++++++++ :doc:`Neuron `, :doc:`Integrate-And-Fire `, :doc:`Adaptive Threshold `, :doc:`Conductance-Based `