Fig. 3

Excitatory regime—phase plane. Phase portrait of system (1) for $I_E=-0.5$, $\lambda =1$, ${\epsilon }_{\Theta }=0.01$, $\omega =4$. The blue line represents the trajectory of the system when starting from initial conditions $({\theta }_0,-\pi )$: it passes along the nullcline $\frac{d{\theta }_E}{dt}=\phi ({\theta }_E,\Theta )=0$ (in red) and then quickly escapes to $(\pi ,{\Theta }_1)$ once past the singular point $(0,{\Theta }_0)$. The dotted purple line shows that, for any starting point $(\Theta ,{\theta }_E)$ where $\Theta <{\Theta }_0$ and ${\theta }_E<{\theta }_0$, the trajectory converges to the blue line