Description
4D model describing the Ott-Antonsen reduction of infinite all-to-all
coupled QIF neurons (Theta-neurons) with Synaptic Depression adaptation
mechanisms [Gastetal_2020]_.
The two state variables :math:`r` and :math:`V` represent the average firing rate and
the average membrane potential of our QIF neurons.
:math:`A` and :math:`B` are respectively the adaptation variable and its derivative.
The equations of the infinite QIF 2D population model read
.. math::
\dot{r} &= 1/\tau (\Delta/(\pi \tau) + 2 V r)\\
\dot{V} &= 1/\tau (V^2 - \tau^2 \pi^2 r^2 + \eta + J \tau r (1 - A) + I)\\
\dot{A} &= 1/\tau_A (B)\\
\dot{B} &= 1/\tau_A (-2 B - A + \alpha r) \\
.. [Gastetal_2020] Gast, R., Schmidt, H., & Knösche, T. R. (2020). A mean-field description of bursting dynamics in spiking neural networks with short-term adaptation. *Neural Computation*, 32(9), 1615-1634.