  With decades of years development, although important progresses have been
made by the pioneers of this field, providing a sophisticated truncation scheme
is still a great challenge up to now if the Dyson-Schwinger Equations(DSEs) of
both quark and gluon propagators (or including even more DSEs) remain after
truncation. In this work we view the coupled reminiscent DSEs of the gluon and
quark propagators after truncation as a system with feedback. Then studying the
stability of this equation array gives useful results. Our calculation shows
that the sum of the gluon and ghost loops plays the most important role in
keeping this system stable and having reasonable solutions. The quark-gluon
vertex plays a relative smaller but also important role. Our method also could
give constraints and inspirations on fabricating a more sophisticated model of
the quark-gluon vertex.
