aeif_cond_beta_multisynapse – Conductance based adaptive exponential integrate-and-fire neuron model ==================================================================================================== Description +++++++++++ ``aeif_cond_beta_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 a beta function. It allows an arbitrary number of synaptic rise time and decay time constants. Synaptic conductance is modeled by a beta 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 two arrays, ``tau_rise`` and ``tau_decay`` for the synaptic rise time and decay time, respectively. The synaptic reversal potentials are supplied by the array ``E_rev``. The 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 `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:`Adaptive Threshold `, :doc:`Integrate-And-Fire `, :doc:`Conductance-Based `