aeif_psc_delta – Current-based adaptive exponential integrate-and-fire neuron model with delta synapse ====================================================================================================== Description +++++++++++ ``aeif_psc_delta`` is the adaptive exponential integrate and fire neuron according to Brette and Gerstner (2005), with postsynaptic currents in the form of delta spikes. 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) - w(t) + I_{syn}(t) + I_e and .. math:: \tau_w \cdot dw/dt= a(V-E_L) - w .. math:: I_{syn}(t) = J \sum_k \delta(t - t^k). Here delta is the Dirac delta function and `k` indexes incoming spikes. This is implemented such that ``V_m`` will be incremented/decremented by the value of `J` after a spike. 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 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 tau_w ms Adaptation time constant Delta_T mV Slope factor tau_w ms Adaptation time constant V_th mV Spike initiation threshold V_peak mV Spike detection threshold ======== ======= ================================== ============= ======= ========================================================= **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 `