aeif_cond_exp – Conductance based exponential integrate-and-fire neuron model ============================================================================= Description +++++++++++ ``aeif_cond_exp`` is the adaptive exponential integrate and fire neuron according to Brette and Gerstner (2005), with postsynaptic conductances in the form of truncated exponentials. This implementation uses the embedded 4th order Runge-Kutta-Fehlberg solver with adaptive stepsize 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)-g_e(t)(V-E_e) \\ -g_i(t)(V-E_i)-w +I_e and .. math:: \tau_w \cdot dw/dt= a(V-E_L) -W Note that the spike detection threshold V_peak is automatically set to :math:`V_th+10 mV` to avoid numerical instabilities that may result from setting V_peak too high. 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 g_in nS Inhibitory synaptic conductance 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 Exponential decay time constant of excitatory synaptic conductance kernel E_in mV Inhibitory reversal potential tau_syn_in ms Exponential decay time constant of inhibitory synaptic conductance kernel =========== ======= =========================================================== ============= ======= ========================================================= **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:`Conductance-Based `