aeif_psc_alpha – Current-based exponential integrate-and-fire neuron model ========================================================================== Description +++++++++++ ``aeif_psc_alpha`` is the adaptive exponential integrate and fire neuron according to Brette and Gerstner (2005). Synaptic currents are modelled as alpha-functions. This implementation uses the embedded 4th order Runge-Kutta-Fehlberg solver with adaptive step size to integrate the differential equation. 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) - w(t) + I_syn(t) + I_e and .. math:: \tau_w \cdot dw/dt= a(V-E_L) - w .. math:: I_{syn}(t) ~ \sum_k (t-t^k) \exp((t-t^k)/\tau_{syn})H(t - t^k) . Here :math:`H(t)` is the Heaviside step function and `k` indexes incoming spikes. For implementation details see the `aeif_models_implementation <../model_details/aeif_models_implementation.ipynb>`_ notebook. See also [1]_. Parameters ++++++++++ The following parameters can be set in the status dictionary. ======== ======= ======================================= **Dynamic state variables:** -------------------------------------------------------- V_m mV Membrane potential I_ex pA Excitatory synaptic current dI_ex pA/ms First derivative of I_ex I_in pA Inhibitory synaptic current dI_in pA/ms First derivative of I_in w pA Spike-adaptation current g 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 ======== ======= ======================================= ======== ======= ================================== **Spike adaptation parameters** --------------------------------------------------- a ns Subthreshold adaptation b pA Spike-triggered adaptation Delta_T mV Slope factor tau_w ms Adaptation time constant V_th mV Spike initiation threshold V_peak mV Spike detection threshold ======== ======= ================================== =========== ======= =========================================================== **Synaptic parameters** ------------------------------------------------------------------------------- tau_syn_ex ms Rise time of excitatory synaptic conductance (alpha function) tau_syn_in ms Rise time of the inhibitory synaptic conductance (alpha function) =========== ======= =========================================================== ============= ======= ========================================================= **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 References ++++++++++ .. [1] Brette R and Gerstner W (2005). Adaptive Exponential Integrate-and-Fire Model as an Effective Description of Neuronal Activity. J Neurophysiol 94:3637-3642. DOI: https://doi.org/10.1152/jn.00686.2005 See also ++++++++ :doc:`Neuron `, :doc:`Adaptive Threshold `, :doc:`Integrate-And-Fire `, :doc:`Current-Based `