8 problems

Consider the two different maximal canards of the nonsmooth system with reset parameter $k$, and let $k$ tend to $0$. In the corresponding smooth slow-fast systems, there is only o…

Let $k$ be the reset parameter, and consider the different maximal canard cycles in the reset-induced nonsmooth system that are exponentially close in parameter space but well sepa…

Consider system … and suppose it has a canard cycle with $N>2$ resets, as described in Proposition 2. Reset-induced canard-cycle doubling conjecture. In some sufficiently small nei…

A planar system is considered in the setting of the paper, with the limit cycles described there and with parameters satisfying suitable conditions. Existence conjecture. There exi…

Subcritical transitory-canard bifurcation conjecture. In the subcritical case, the system possesses a saddle-node bifurcation of transitory canard cycles for $k=1$.

Transitory canard cycles conjecture. There exist values of $\varepsilon>0$ and $k\approx 1$ such that the corresponding system exhibits one, two, or three canard limit cycles in a…

Canard-cycle conjecture. For every desired number $l\in\mathbb{N}$ there exists a local topologically generic set of systems such that the slow curve is nondegenerate and simple un…

Consider generic slow-fast systems on the two-torus with one time-scaling parameter $\varepsilon$. In the previously studied setting, there is a sequence of intervals accumulating…