On singular equilibria of index-1 DAEs

Some qualitative properties of singular equilibria arising in semiexplicit index-1 differential-algebraic equations are discussed in this paper. We ex tend a taxonomy of singularities from index-0 problems to address situation s not covered by the singularity induced bifurcation, singular flow, and as sociated theorems. Although some related phenomena may occur, different beh avior can be expected when the assumptions supporting these results are not satisfied, as is illustrated by several examples. Special attention is pai d to the effect that the singular nature of the underlying ordinary differe ntial equation and, eventually, of the solution manifold, has on the behavi or of the original singular index-1 problem.