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\[ \begin{aligned} \text{Firing-rates:} && \dot{U_e} &= \frac{1}{\tau_e}\big\{ -U_e + \color{cyan}{r_e} f\big[A_e - \theta_e + g_e S(t) - \beta_e V_e\big] \big\} \color{cyan}{+ D_{U_e}\nabla^2U_e} \\&& \dot{U_i} &= \frac{1}{\tau_i}\big\{ -U_i + \color{cyan}{r_i} f\left[A_i - \theta_i + g_i S(t) - \beta_i V_i \right] \big\} \color{cyan}{+ D_{U_i}\nabla^2U_i} \\ \text{Synaptic activations:}&& A_e &= (w_{ee} K_l + a_{ee} K_e) \star U_e - (w_{ie} K_l + a_{ie} K_i) \star U_i \\&& A_i &= (w_{ei}K_l +a_{ei} K_e) \star U_e - (w_{ii}K_l + a_{ii} K_i) \star U_i \\ \text{Synaptic adaptation:}&& \dot{V_e} &= \frac{1}{\tau_{ve}}(U_e - V_e) \color{cyan}{+ D_{V_e}\nabla^2V_e},\,\, \text{ where }\tau_{ve} = \begin{cases} \alpha_e & \text{if }V_e< U_e \\ \gamma_e & \text{if }V_e\ge U_e \end{cases} \\&& \dot{V_i} &= \frac{1}{\alpha_i}(U_i - V_i) \color{cyan}{+ D_{V_i}\nabla^2V_i} \\ \text{Interaction kernels:}&& K_{e,i,l}(x,y) &\propto \exp\big(\frac{1}{2} \tfrac{x^2}{\sigma_{e,i,l}^2} +\tfrac{1}{2} \frac{y^2}{\sigma_{e,i,l}^2}\big) \\&& \color{cyan}{\text{Cyan: }}&\color{cyan}{\text{extended terms to support reaction-diffusion}} \end{aligned} \]