Decomposition of Lorenz Trajectories Based on Space Curve Tangent Vector
This article explores the evolution of Lorenz trajectories within attractors. Specifically, based on the characteristics of the tangents to trajectories, we derive quantitative standards for determining the spatial position of trajectory lines. The Lorenz trajectory is decomposed into four parts. Th...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-03-01
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| Series: | Atmosphere |
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| Online Access: | https://www.mdpi.com/2073-4433/15/3/319 |
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| author | Jingru Ma Lei Hu Hongke She Binghuai Fan Chaojiu Da |
| author_facet | Jingru Ma Lei Hu Hongke She Binghuai Fan Chaojiu Da |
| author_sort | Jingru Ma |
| collection | DOAJ |
| description | This article explores the evolution of Lorenz trajectories within attractors. Specifically, based on the characteristics of the tangents to trajectories, we derive quantitative standards for determining the spatial position of trajectory lines. The Lorenz trajectory is decomposed into four parts. This standard is objective and quantitative and is independent of the initial field of the Lorenz equation and the calculation scheme; importantly, it is designed based on the inherent dynamic characteristics of the Lorenz equation. Linear fitting of the trajectories in the left and right equilibrium point regions shows that the trajectories lie on planes, indicating the existence of linear features in the nonlinear system. This study identifies the fundamental causes of chaos in the Lorenz equation using the microscopic evolution and local characteristics of the trajectories, and indicating that the spatial position of the initial field is important for their predictability. We theoretically demonstrate that mutation is essentially self-regulation within chaotic systems. This scheme is designed according to the evolution characteristics of Lorenz trajectories, and thus has certain methodological limitations that mean it may not be applicable to other chaotic systems. However, it does depict the causes of chaos and elucidates the sensitivity of differential equations to initial values in terms of trajectory evolution. |
| first_indexed | 2024-04-24T18:34:45Z |
| format | Article |
| id | doaj.art-b844c29064b34b178640f80cbc1c43a8 |
| institution | Directory Open Access Journal |
| issn | 2073-4433 |
| language | English |
| last_indexed | 2024-04-24T18:34:45Z |
| publishDate | 2024-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Atmosphere |
| spelling | doaj.art-b844c29064b34b178640f80cbc1c43a82024-03-27T13:20:41ZengMDPI AGAtmosphere2073-44332024-03-0115331910.3390/atmos15030319Decomposition of Lorenz Trajectories Based on Space Curve Tangent VectorJingru Ma0Lei Hu1Hongke She2Binghuai Fan3Chaojiu Da4School of Mathematics and Computer Science Institute, Northwest Minzu University, Lanzhou 730030, ChinaSchool of Mathematics and Computer Science Institute, Northwest Minzu University, Lanzhou 730030, ChinaSchool of Mathematics and Computer Science Institute, Northwest Minzu University, Lanzhou 730030, ChinaSchool of Mathematics and Computer Science Institute, Northwest Minzu University, Lanzhou 730030, ChinaSchool of Mathematics and Computer Science Institute, Northwest Minzu University, Lanzhou 730030, ChinaThis article explores the evolution of Lorenz trajectories within attractors. Specifically, based on the characteristics of the tangents to trajectories, we derive quantitative standards for determining the spatial position of trajectory lines. The Lorenz trajectory is decomposed into four parts. This standard is objective and quantitative and is independent of the initial field of the Lorenz equation and the calculation scheme; importantly, it is designed based on the inherent dynamic characteristics of the Lorenz equation. Linear fitting of the trajectories in the left and right equilibrium point regions shows that the trajectories lie on planes, indicating the existence of linear features in the nonlinear system. This study identifies the fundamental causes of chaos in the Lorenz equation using the microscopic evolution and local characteristics of the trajectories, and indicating that the spatial position of the initial field is important for their predictability. We theoretically demonstrate that mutation is essentially self-regulation within chaotic systems. This scheme is designed according to the evolution characteristics of Lorenz trajectories, and thus has certain methodological limitations that mean it may not be applicable to other chaotic systems. However, it does depict the causes of chaos and elucidates the sensitivity of differential equations to initial values in terms of trajectory evolution.https://www.mdpi.com/2073-4433/15/3/319Lorenz equationtangent vectorequilibrium statedecomposition of trajectoriesdata fitting |
| spellingShingle | Jingru Ma Lei Hu Hongke She Binghuai Fan Chaojiu Da Decomposition of Lorenz Trajectories Based on Space Curve Tangent Vector Atmosphere Lorenz equation tangent vector equilibrium state decomposition of trajectories data fitting |
| title | Decomposition of Lorenz Trajectories Based on Space Curve Tangent Vector |
| title_full | Decomposition of Lorenz Trajectories Based on Space Curve Tangent Vector |
| title_fullStr | Decomposition of Lorenz Trajectories Based on Space Curve Tangent Vector |
| title_full_unstemmed | Decomposition of Lorenz Trajectories Based on Space Curve Tangent Vector |
| title_short | Decomposition of Lorenz Trajectories Based on Space Curve Tangent Vector |
| title_sort | decomposition of lorenz trajectories based on space curve tangent vector |
| topic | Lorenz equation tangent vector equilibrium state decomposition of trajectories data fitting |
| url | https://www.mdpi.com/2073-4433/15/3/319 |
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