aeif_psc_exp – Current-based exponential integrate-and-fire neuron model ======================================================================== Description +++++++++++ aeif_psc_exp is the adaptive exponential integrate and fire neuron according to Brette and Gerstner (2005), with postsynaptic currents 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*\Delta_T*\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 * 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 instabilites that may result from setting V_peak too high. For implementation details see the `aeif_models_implementation <../neuron_docs/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 I_ex pA Excitatory synaptic current I_in pA Inhibitory synaptic current 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_t mV Spike initiation threshold V_peak mV Spike detection threshold ======== ======= ================================== =========== ======= =========================================================== **Synaptic parameters** ------------------------------------------------------------------------------- tau_syn_ex ms Exponential decay time constant of excitatory synaptic conductance kernel 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:`Integrate-And-Fire `, :doc:`Adaptive Threshold `, :doc:`Current-Based `