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\[ \begin{aligned} \text{Firing-rates:} && \tau_e \dot{U_e} &= -U_e + f\left[ D _e - \theta_e + g_e S(t) - \beta_e V_e\right] \\&& \tau_i \dot{U_i} &= -U_i + f\left[ D_i - \theta_i + g_i S(t) - \beta_i V_i \right] \\ \text{Synaptic drives:}&& D_e &= (w_{ee} K_l + a_{ee} K_e) \star U_e - (w_{ie} K_l + a_{ie} K_i) \star U_i \\&& D_i &= (w_{ei}K_l +a_{ei} K_e) \star U_e - (w_{ii}K_l + a_{ii} K_i) \star U_i \\ \text{Synaptic adaptation:}&& \tau_{ve} \dot{V_e} &= U_e - V_e,\,\, \tau_{ve} = \begin{cases} \alpha_e & \text{if }V_e< U_e \\ \gamma_e & \text{if }V_e\ge U_e \end{cases} \\&& \alpha_i \dot{V_i} &= U_i - V_i \\ \text{Interaction kernels:}&& K_{e,i,l}(x,y) &\propto \exp\big(\tfrac{1}{2} \tfrac{x^2}{\sigma_{e,i,l}^2} +\tfrac{1}{2} \tfrac{y^2}{\sigma_{e,i,l}^2}\big) \end{aligned} \]