Circuit induced oscillations of SNDC semiconductors

A highly degenerate nilpotent singularity is determined in the equations governing the dynamics of the current in an electrical circuit that contains an SNDC semiconductor element. Experimentally relevant features of the resulting unfolding theory are outlined and supplemented with numerical simulations. The interplay between stable and unstable current oscillations can produce complicated bifurcation sequences which have not been described so far. These include hysteric transitions to bi- and tristability, the coalescence of a stable and an unstable oscillation and homoclinic connections.