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Bifurcation analyses of nonlinear dynamical systems : From theory to numerical computations
https://tokushima-u.repo.nii.ac.jp/records/2007842
https://tokushima-u.repo.nii.ac.jp/records/20078422f4afd83-a593-4151-9536-1293267d7fec
| 名前 / ファイル | ライセンス | アクション |
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nolta_3_4_458.pdf (603 KB)
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| Item type | 文献 / Documents(1) | |||||||||||||||||||||||
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| 公開日 | 2020-07-13 | |||||||||||||||||||||||
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| アクセス権 | open access | |||||||||||||||||||||||
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| 資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||||||||||||||||||||
| 資源タイプ | journal article | |||||||||||||||||||||||
| 出版社版DOI | ||||||||||||||||||||||||
| 関連識別子 | https://doi.org/10.1587/nolta.3.458 | |||||||||||||||||||||||
| 関連名称 | 10.1587/nolta.3.458 | |||||||||||||||||||||||
| 出版タイプ | ||||||||||||||||||||||||
| 出版タイプ | VoR | |||||||||||||||||||||||
| 出版タイプResource | http://purl.org/coar/version/c_970fb48d4fbd8a85 | |||||||||||||||||||||||
| タイトル | ||||||||||||||||||||||||
| タイトル | Bifurcation analyses of nonlinear dynamical systems : From theory to numerical computations | |||||||||||||||||||||||
| 著者 |
津元, 国親
× 津元, 国親
× 上田, 哲史
WEKO
98
× 吉永, 哲哉
WEKO
1587
× 川上, 博 |
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| 内容記述 | In this paper, we explain how to compute bifurcation parameter values of periodic solutions for non-autonomous nonlinear differential equations. Although various approaches and tools are available for solving this problem nowadays, we have devised a very simple method composed only of basic computational algorithms appearing in textbooks for beginner's, i.e., Newton's method and the Runge-Kutta method. We formulate the bifurcation problem as a boundary value problem and use Newton's method as a solver consistently. All derivatives required in each iteration are obtained by solving variational equations about the state and the parameter. Thanks to the quadratic convergence ability of Newton's method, accurate results can be quickly and effectively obtained without using any sophisticated mathematical library or software. If a discontinuous periodic force is applied to the system, we can use the same strategy to solve the bifurcation problem. The key point of this method is deriving a differentiable composite map from the various information about the problem such as the location of sections, the periodicity, the Poincaré mapping, etc. | |||||||||||||||||||||||
| キーワード | ||||||||||||||||||||||||
| 主題 | nonlinear dynamical system | |||||||||||||||||||||||
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| 主題 | bifurcation | |||||||||||||||||||||||
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| 主題 | boundary value problem | |||||||||||||||||||||||
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| 主題 | variational equation | |||||||||||||||||||||||
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| 主題 | Newton's method | |||||||||||||||||||||||
| 書誌情報 |
en : Nonlinear Theory and Its Applications, IEICE 巻 3, 号 4, p. 458-476, 発行日 2012-10-01 |
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| 収録物識別子タイプ | ISSN | |||||||||||||||||||||||
| 収録物識別子 | 21854106 | |||||||||||||||||||||||
| 出版者 | ||||||||||||||||||||||||
| 出版者 | The Institute of Electronics, Information and Communication Engineers | |||||||||||||||||||||||
| 権利情報 | ||||||||||||||||||||||||
| 権利情報 | © IEICE 2012 | |||||||||||||||||||||||
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| 識別子 | 248207 | |||||||||||||||||||||||
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| 言語 | eng | |||||||||||||||||||||||
