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With decades of years development, although important progresses have beenmade by the pioneers of this field, providing a sophisticated truncation schemeis still a great challenge up to now if the Dyson-Schwinger Equations(DSEs) ofboth quark and gluon propagators (or including even more DSEs) remain aftertruncation. In this work we view the coupled reminiscent DSEs of the gluon andquark propagators after truncation as a system with feedback. Then studying thestability of this equation array gives useful results. Our calculation showsthat the sum of the gluon and ghost loops plays the most important role inkeeping this system stable and having reasonable solutions. The quark-gluonvertex plays a relative smaller but also important role. Our method also couldgive constraints and inspirations on fabricating a more sophisticated model ofthe quark-gluon vertex.

System stability and truncation schemes to the Dyson-Schwinger Equations