On refinement of the generalized Bendixson theorem

Zhong Zhi Bai; Wen Ting Wu

doi:10.1016/j.apnum.2020.09.021

On refinement of the generalized Bendixson theorem

Zhong Zhi Bai, Wen Ting Wu^*

^*Corresponding author for this work

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	125-138
Number of pages	14
Journal	Applied Numerical Mathematics
Volume	164
DOIs	https://doi.org/10.1016/j.apnum.2020.09.021
Publication status	Published - Jun 2021

Keywords

Bendixson theorem
Eigenvalue distribution
Generalized Bendixson theorem
Matrix pair
Refinement

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10.1016/j.apnum.2020.09.021

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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.",

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KW - Eigenvalue distribution

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KW - Matrix pair

KW - Refinement

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On refinement of the generalized Bendixson theorem

Abstract

Keywords

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