Fig. 10

Nonsingular canards and global trajectories. The true nonsingular canard (blue) for the three-dimensional modified propofol model is located for ${\tau }_s=15$. This canard is then continued in ${\tau }_s$ using a suitable boundary condition problem. We thus obtain the true canard for any value of ${\tau }_s$. This true canard is compared to the corresponding trajectory (black) of the three-dimensional modified propofol model. Here, we see that the true nonsingular canard correctly bounds the trajectories into spiking and quiescent regimes. The folded singularity (purple) and ${\mathbf{eq}}_3$ (green) are indicated. a The nonsingular trajectory and associated canard for ${\tau }_s=8$ in $(v,w)$-space. b The nonsingular trajectory and associated canard for ${\tau }_s=9$ in $(v,w)$-space