Jacobi Stability for T-System
In this paper will be considered a three-dimensional autonomous quadratic polynomial system of first-order differential equations with three real parameters, the so-called T-system. This system is symmetric relative to the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-01-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/16/1/84 |
| _version_ | 1797342521933692928 |
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| author | Florian Munteanu |
| author_facet | Florian Munteanu |
| author_sort | Florian Munteanu |
| collection | DOAJ |
| description | In this paper will be considered a three-dimensional autonomous quadratic polynomial system of first-order differential equations with three real parameters, the so-called T-system. This system is symmetric relative to the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>O</mi><mi>z</mi></mrow></semantics></math></inline-formula>-axis and represents a special type of the generalized Lorenz system. The approach of this work will consist of the study of the nonlinear dynamics of this system through the Kosambi–Cartan–Chern (KCC) geometric theory. More exactly, we will focus on the associated system of second-order differential equations (SODE) from the point of view of Jacobi stability by determining the five invariants of the KCC theory. These invariants determine the internal geometrical characteristics of the system, and particularly, the deviation curvature tensor is decisive for Jacobi stability. Furthermore, we will look for necessary and sufficient conditions that the system parameters must satisfy in order to have Jacobi stability for every equilibrium point. |
| first_indexed | 2024-03-08T10:34:02Z |
| format | Article |
| id | doaj.art-09d351c399674afcb4c99acb81909470 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-08T10:34:02Z |
| publishDate | 2024-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-09d351c399674afcb4c99acb819094702024-01-26T18:38:51ZengMDPI AGSymmetry2073-89942024-01-011618410.3390/sym16010084Jacobi Stability for T-SystemFlorian Munteanu0Department of Applied Mathematics, Faculty of Sciences, University of Craiova, Al. I. Cuza, 13, 200585 Craiova, RomaniaIn this paper will be considered a three-dimensional autonomous quadratic polynomial system of first-order differential equations with three real parameters, the so-called T-system. This system is symmetric relative to the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>O</mi><mi>z</mi></mrow></semantics></math></inline-formula>-axis and represents a special type of the generalized Lorenz system. The approach of this work will consist of the study of the nonlinear dynamics of this system through the Kosambi–Cartan–Chern (KCC) geometric theory. More exactly, we will focus on the associated system of second-order differential equations (SODE) from the point of view of Jacobi stability by determining the five invariants of the KCC theory. These invariants determine the internal geometrical characteristics of the system, and particularly, the deviation curvature tensor is decisive for Jacobi stability. Furthermore, we will look for necessary and sufficient conditions that the system parameters must satisfy in order to have Jacobi stability for every equilibrium point.https://www.mdpi.com/2073-8994/16/1/84T-systemthe deviation curvature tensorJacobi stabilityKCC geometric theory |
| spellingShingle | Florian Munteanu Jacobi Stability for T-System Symmetry T-system the deviation curvature tensor Jacobi stability KCC geometric theory |
| title | Jacobi Stability for T-System |
| title_full | Jacobi Stability for T-System |
| title_fullStr | Jacobi Stability for T-System |
| title_full_unstemmed | Jacobi Stability for T-System |
| title_short | Jacobi Stability for T-System |
| title_sort | jacobi stability for t system |
| topic | T-system the deviation curvature tensor Jacobi stability KCC geometric theory |
| url | https://www.mdpi.com/2073-8994/16/1/84 |
| work_keys_str_mv | AT florianmunteanu jacobistabilityfortsystem |