aeif_cond_alpha – Conductance based exponential integrate-and-fire neuron model =============================================================================== Description +++++++++++ ``aeif_cond_alpha`` is the adaptive exponential integrate and fire neuron according to Brette and Gerstner (2005). Synaptic conductances 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_m \frac{dV}{dt} = -g_L(V-E_L)+g_L\Delta_T\exp\left(\frac{V-V_{th}}{\Delta_T}\right) - g_e(t)(V-E_e) \\ -g_i(t)(V-E_i)-w +I_e and .. math:: \tau_w \frac{dw}{dt} = a(V-E_L) - w 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 g_ex nS Excitatory synaptic conductance dg_ex nS/ms First derivative of g_ex g_in nS Inhibitory synaptic conductance dg_in nS/ms First derivative of g_in 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 ======== ======= ======================================= ======== ======= ================================== **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** ------------------------------------------------------------------------------- E_ex mV Excitatory reversal potential tau_syn_ex ms Rise time of excitatory synaptic conductance (alpha function) E_in mV Inhibitory reversal potential 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. Journal of Neurophysiology. 943637-3642 DOI: https://doi.org/10.1152/jn.00686.2005 See also ++++++++ :doc:`Neuron `, :doc:`Integrate-And-Fire `, :doc:`Adaptive Threshold `, :doc:`Conductance-Based `