Primary-canard and exponentially narrow transition conjecture

Let $\bar\mu(\varepsilon)$ be a parameter function for the canonical three-dimensional system, and let $\bar\mu_0=-\frac{a(a+b)}{2b^2}$. Primary-canard transition conjecture. There exists a function $\bar\mu(\varepsilon)$ such that, for $\bar\mu=\bar\mu(\varepsilon)$, the system has a primary $S_{1D}$ canard; the transition from mixed-mode oscillations to spiking occurs within an exponentially small interval $O(e^{-c/\varepsilon})$, with $c>0$, about $\bar\mu(\varepsilon)$; and $\bar\mu(0)=\bar\mu_0=-\frac{a(a+b)}{2b^2}$. This combines the conjectured persistence and uniqueness of the singular canard with the predicted exponentially narrow transition.