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 [1]_, with postsynaptic currents in the form of delta spikes. This implementation uses the embedded 5th order Runge-Kutta solver with adaptive stepsize 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(t)- w + I_e and .. math:: \tau_w dw/dt= a(V-E_L) -w .. math:: I(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. .. note:: The number of receptor ports must be specified at neuron creation (default value is 1) and the receptor index starts from 0 (and not from 1 as in NEST models). The time constants are supplied by an array, ``tau_syn``. Port numbers are automatically assigned in the range 0 to ``n_receptors-1``. During connection, the ports are selected with the synapse property ``receptor``. 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** ---------------------------------------------------------- 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 ======== ======= ================================== ============= ======= ========================================================= **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 `