Conjecture on the connection of periodic-orbit families in case $VI_3^\epsilon$

Consider the regularized planar piecewise smooth system in case $VI_3^\epsilon$, with the two families of periodic orbits obtained respectively in Proposition~ and Proposition~. Periodic-orbit connection conjecture. The two families of periodic orbits in $VI_3^\epsilon$ belong to the same family of locally unique periodic orbits. This conjecture concerns whether the small periodic orbits connect to the larger periodic orbits associated with the canard explosion. The preceding discussion indicates that proving this would require an analysis analogous to the classical canard-explosion analysis, complicated here by the nontrivial dependence of the Hamiltonian function on the regularization function.