Abstract 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.

中文翻译：

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广义本迪克森定理的细化

摘要 我们进一步改进和扩展了 Bai 和 Ng (Numer. Math. 96 (2003) 197-220) 给出的结果，获得了关于复方矩阵对的广义 Bendixson 定理的完整版本。通过放宽这些界限，我们还提供了这个广义 Bendixson 定理的一些简化版本，它们的描述更直观，应用更方便。