Fundamental Structure of General Stochastic Dynamical Systems: High-Dimension Case
No one has proved that mathematically general stochastic dynamical systems have a special structure. Thus, we introduce a structure of a general stochastic dynamical system. According to scientific understanding, we assert that its deterministic part can be decomposed into three significant parts: t...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/2596074 |
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| _version_ | 1850157498094321664 |
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| author | Haoyu Wang Xiaoliang Gan Wenqing Hu Ping Ao |
| author_facet | Haoyu Wang Xiaoliang Gan Wenqing Hu Ping Ao |
| author_sort | Haoyu Wang |
| collection | DOAJ |
| description | No one has proved that mathematically general stochastic dynamical systems have a special structure. Thus, we introduce a structure of a general stochastic dynamical system. According to scientific understanding, we assert that its deterministic part can be decomposed into three significant parts: the gradient of the potential function, friction matrix and Lorenz matrix. Our previous work proved this structure for the low-dimension case. In this paper, we prove this structure for the high-dimension case. Hence, this structure of general stochastic dynamical systems is fundamental. |
| format | Article |
| id | doaj-art-35109291a9fc4ac7b79ae7ccc4ae704f |
| institution | OA Journals |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-35109291a9fc4ac7b79ae7ccc4ae704f2025-08-20T02:24:08ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/2596074Fundamental Structure of General Stochastic Dynamical Systems: High-Dimension CaseHaoyu Wang0Xiaoliang Gan1Wenqing Hu2Ping Ao3Department of MathematicsSchool of Mathematics and Computing ScienceDepartment of MathematicsDepartment of PhysicsNo one has proved that mathematically general stochastic dynamical systems have a special structure. Thus, we introduce a structure of a general stochastic dynamical system. According to scientific understanding, we assert that its deterministic part can be decomposed into three significant parts: the gradient of the potential function, friction matrix and Lorenz matrix. Our previous work proved this structure for the low-dimension case. In this paper, we prove this structure for the high-dimension case. Hence, this structure of general stochastic dynamical systems is fundamental.http://dx.doi.org/10.1155/2022/2596074 |
| spellingShingle | Haoyu Wang Xiaoliang Gan Wenqing Hu Ping Ao Fundamental Structure of General Stochastic Dynamical Systems: High-Dimension Case Journal of Mathematics |
| title | Fundamental Structure of General Stochastic Dynamical Systems: High-Dimension Case |
| title_full | Fundamental Structure of General Stochastic Dynamical Systems: High-Dimension Case |
| title_fullStr | Fundamental Structure of General Stochastic Dynamical Systems: High-Dimension Case |
| title_full_unstemmed | Fundamental Structure of General Stochastic Dynamical Systems: High-Dimension Case |
| title_short | Fundamental Structure of General Stochastic Dynamical Systems: High-Dimension Case |
| title_sort | fundamental structure of general stochastic dynamical systems high dimension case |
| url | http://dx.doi.org/10.1155/2022/2596074 |
| work_keys_str_mv | AT haoyuwang fundamentalstructureofgeneralstochasticdynamicalsystemshighdimensioncase AT xiaolianggan fundamentalstructureofgeneralstochasticdynamicalsystemshighdimensioncase AT wenqinghu fundamentalstructureofgeneralstochasticdynamicalsystemshighdimensioncase AT pingao fundamentalstructureofgeneralstochasticdynamicalsystemshighdimensioncase |