On refinement of the generalized Bendixson theorem

摘要

We further refine and extend the results given by Bai and Ng (Numer. Math. 96 (2003) 197-220), obtaining a complete version of the generalized Bendixson theorem with respect to a square complex matrix pair. By relaxing these bounds we also provide a few simplified versions of this generalized Bendixson theorem, which are more intuitive in description and more convenient in application.