E-cell firing rate ∈[0,1]

I-cell firing rate ∈[0,1]

E/I trajectories in phase space
Steady-state adaptation

Firing rate variables
Red=E Green=I Blue=|E-I|

Adaptation variables
Red=I Green=E Blue=|E-I|

E/I trajectories in phase space
With, without adaptation

\[\textrm{E-cells: } \tau_e \dot{U_e} = -U_e + f( a_{ee} \cdot K_e \star U_e - a_{ie} \cdot K_i \star U_i - \theta_e + g_e S(t) - \beta_e V_e)\] \[\textrm{I-cells: } \tau_i \dot{U_i} = -U_i + f( a_{ei} \cdot K_e \star U_e - a_{ii} \cdot K_i \star U_i - \theta_i + g_i S(t) - \beta_i V_i )\] \[\textrm{E-cell adaptation: } \tau_{ve} \dot{V_e} = U_e - V_e,\,\, \tau_{ve} = \begin{cases} \alpha_e & \text{if }V_e< U_e \\ \gamma_e & \text{if }V_e\ge U_e\end{cases} \] \[\textrm{I-cell adaptation: } \alpha_i \dot{V_i} = U_i - V_i \] \[\textrm{Interaction kernel (normalized to 1): } K_{e,i}(x,y) \propto \exp\left(\frac{1}{2} \frac{x^2}{\sigma_{x\,e,i}^2}+\frac{1}{2} \frac{y^2}{\sigma_{y\,e,i}^2}\right)\]