aeif_cond_alpha – Conductance-based adaptive exponential integrate-and-fire neuron model ======================================================================================== Description +++++++++++ ``aeif_cond_alpha`` is a conductance-based adaptive exponential integrate-and-fire neuron model according to [1]_ with synaptic conductance modeled by an alpha function, as described in [2]_ 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) + g_{ex}(t) (V - E_{rev\_ ex,i}) + g_{in}(t) (V - E_{rev\_ in,i}) - w + I_e The differential equation for the spike-adaptation current `w` is .. math:: \tau_w dw/dt = a(V - E_L) - w When the neuron fires a spike, the adaptation current :math:`w <- w + b`. .. note:: Although this 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 g_ex nS Excitatory synaptic conductance g_in nS Inhibitory synaptic conductance 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** ---------------------------------------------------------------------------------- E_rev_ex mV Excitatory reversal potential E_rev_in mV Inhibitory reversal potential tau_syn_ex ms Time constant of excitatory synaptic conductance tau_syn_in 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. Journal of Neurophysiology. 943637-3642 DOI: https://doi.org/10.1152/jn.00686.2005 .. [2] A. Roth and M. C. W. van Rossum, Computational Modeling Methods for Neuroscientists, MIT Press 2013, Chapter 6. DOI: https://doi.org/10.7551/mitpress/9780262013277.003.0007 See also +++++++ :doc:`Neuron `, :doc:`Integrate-And-Fire `, :doc:`Adaptive Threshold `, :doc:`Conductance-Based `