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 [1]_. Synaptic currents are modeled as alpha functions. This implementation uses the 5th order Runge-Kutta 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) + I_{syn\_ ex}(V, t) - I_{syn\_ in}(V, t) - w + I_e where `I_syn_ex` and `I_syn_in` are the excitatory and inhibitory synaptic currents modeled as alpha functions. The differential equation for the spike-adaptation current `w` is: .. math:: \tau_w dw/dt= a(V-E_L) - w .. note:: Although this model is not multisynapse, the port (excitatory or inhibitory) to be chosen must be specified using the synapse property ``receptor``. The excitatory port has index 0, whereas the inhibitory one has index 1. Differently from NEST, the connection weights related to the inhibitory port must be positive. Parameters ++++++++++ The following parameters can be set in the status dictionary. ========== ======= ======================================= **Dynamic state variables:** ---------------------------------------------------------- V_m mV Membrane potential I_syn_ex pA Excitatory synaptic current I_syn_in pA Inhibitory synaptic current w pA Spike-adaptation current ========== ======= ======================================= ========== ======= ======================================= **Membrane Parameters** ---------------------------------------------------------- V_th mV Spike initiation threshold Delta_T mV Slope factor g_L nS Leak conductance E_L mV Leak reversal potential C_m pF Capacity of the membrane I_e pA Constant external input current V_peak mV Spike detection threshold V_reset mV Reset value for V_m after a spike t_ref ms Duration of refractory period den_delay ms Dendritic delay ========== ======= ======================================= ======== ======= ================================== **Spike adaptation parameters** --------------------------------------------------- a ns Subthreshold adaptation b pA Spike-triggered adaptation tau_w ms Adaptation time constant ======== ======= ================================== =========== ======= =========================================================== **Synaptic parameters** ------------------------------------------------------------------------------- tau_syn_ex ms Time constant of excitatory synaptic conductance tau_syn_ex ms Time constant of inhibitory synaptic conductance =========== ======= =========================================================== ============= ======= ========================================================= **Integration parameters** ------------------------------------------------------------------------------- h0_rel real Starting step in ODE integration relative to time resolution h_min_rel real Minimum step in ODE integration relative to time resolution ============= ======= ========================================================= 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 `