  In this article we prove that for locally defined singular SU(n+1) Toda
systems in R^2, the profile of fully bubbling solutions near the singular
source can be accurately approximated by global solutions. The main ingredients
of our new approach are the classification theorem of Lin-Wei-Ye and the
non-degeneracy of the linearized Toda system, which make us overcome the
difficulties that come from the lack of symmetry and the singular source.

Analysis of PDEs