On the effect of invisibility of stable periodic orbits at homoclinic bifurcations

► Single-round sinks emerge out of homoclinic tangency to a saddle-focus. ► Bifurcation diagram has a “comb-like” structure. ► When sectional dissipativity is broken, sinks do not disappear, but become invisible. ► One-parameter cascade of single-round sinks may have zero probability.