Stability of the Planar Quadratic Systems from the Ring-Theoretic Viewpoint
We show that the classical result on the stability of the origin in a quadratic planar system of ODEs can be formulated using either matrix theory or via its associated real and complex Marcus algebra. A generalization to a three-dimensional case is considered and some counterexamples provided.
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-05-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/10/1629 |
| _version_ | 1827668048124837888 |
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| author | Borut Zalar Matej Mencinger |
| author_facet | Borut Zalar Matej Mencinger |
| author_sort | Borut Zalar |
| collection | DOAJ |
| description | We show that the classical result on the stability of the origin in a quadratic planar system of ODEs can be formulated using either matrix theory or via its associated real and complex Marcus algebra. A generalization to a three-dimensional case is considered and some counterexamples provided. |
| first_indexed | 2024-03-10T03:29:42Z |
| format | Article |
| id | doaj.art-3621ae635bec44d6bcf86fecf74a33d3 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T03:29:42Z |
| publishDate | 2022-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-3621ae635bec44d6bcf86fecf74a33d32023-11-23T12:00:04ZengMDPI AGMathematics2227-73902022-05-011010162910.3390/math10101629Stability of the Planar Quadratic Systems from the Ring-Theoretic ViewpointBorut Zalar0Matej Mencinger1Faculty of Civil Engineering, Transportation Engineering and Architecture, University of Maribor, 2000 Maribor, SloveniaFaculty of Civil Engineering, Transportation Engineering and Architecture, University of Maribor, 2000 Maribor, SloveniaWe show that the classical result on the stability of the origin in a quadratic planar system of ODEs can be formulated using either matrix theory or via its associated real and complex Marcus algebra. A generalization to a three-dimensional case is considered and some counterexamples provided.https://www.mdpi.com/2227-7390/10/10/1629quadratic differential systemscommutative nonassociative algebrasingular pointsstability |
| spellingShingle | Borut Zalar Matej Mencinger Stability of the Planar Quadratic Systems from the Ring-Theoretic Viewpoint Mathematics quadratic differential systems commutative nonassociative algebra singular points stability |
| title | Stability of the Planar Quadratic Systems from the Ring-Theoretic Viewpoint |
| title_full | Stability of the Planar Quadratic Systems from the Ring-Theoretic Viewpoint |
| title_fullStr | Stability of the Planar Quadratic Systems from the Ring-Theoretic Viewpoint |
| title_full_unstemmed | Stability of the Planar Quadratic Systems from the Ring-Theoretic Viewpoint |
| title_short | Stability of the Planar Quadratic Systems from the Ring-Theoretic Viewpoint |
| title_sort | stability of the planar quadratic systems from the ring theoretic viewpoint |
| topic | quadratic differential systems commutative nonassociative algebra singular points stability |
| url | https://www.mdpi.com/2227-7390/10/10/1629 |
| work_keys_str_mv | AT borutzalar stabilityoftheplanarquadraticsystemsfromtheringtheoreticviewpoint AT matejmencinger stabilityoftheplanarquadraticsystemsfromtheringtheoreticviewpoint |