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Nonlinear resonance and devil’s staircase in a forced planer system containing a piecewise linear hysteresis
https://tokushima-u.repo.nii.ac.jp/records/2005062
https://tokushima-u.repo.nii.ac.jp/records/2005062331c15b7-7cb0-42cd-8f70-4bc7e8f9472b
| 名前 / ファイル | ライセンス | アクション |
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chaossf_111_75.pdf (2.97 MB)
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| Item type | 文献 / Documents(1) | |||||||||||||||||
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| 公開日 | 2018-07-05 | |||||||||||||||||
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| アクセス権 | open access | |||||||||||||||||
| 資源タイプ | ||||||||||||||||||
| 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/10.1016/j.chaos.2018.04.007 | |||||||||||||||||
| 関連名称 | 10.1016/j.chaos.2018.04.007 | |||||||||||||||||
| 出版タイプ | ||||||||||||||||||
| 出版タイプ | AM | |||||||||||||||||
| 出版タイプResource | http://purl.org/coar/version/c_ab4af688f83e57aa | |||||||||||||||||
| タイトル | ||||||||||||||||||
| タイトル | Nonlinear resonance and devil’s staircase in a forced planer system containing a piecewise linear hysteresis | |||||||||||||||||
| 著者 |
ミイノ, ユウ
× ミイノ, ユウ
× 上田, 哲史
WEKO
98
× 川上, 博 |
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| 抄録 | ||||||||||||||||||
| 内容記述 | The Duffing equation describes a periodically forced oscillator model with a nonlinear elasticity. In its circuitry, a saturable-iron core often exhibits a hysteresis, however, a few studies about the Duffing equation has discussed the effects of the hysteresis because of difficulties in their mathematical treatment. In this paper, we investigate a forced planer system obtained by replacing a cubic term in the Duffing equation with a hysteresis function. For simplicity, we approximate the hysteresis to a piecewise linear function. Since the solutions are expressed by combinations of some dynamical systems and switching conditions, a finite-state machine is derived from the hybrid system approach, and then bifurcation theory can be applied to it. We topologically classify periodic solutions and compute local and grazing bifurcation sets accurately. In comparison with the Duffing equation, we discuss the effects caused by the hysteresis, such as the devil’s staircase in resonant solutions. | |||||||||||||||||
| キーワード | ||||||||||||||||||
| 主題 | bifurcation analysis | |||||||||||||||||
| キーワード | ||||||||||||||||||
| 主題 | hybrid system | |||||||||||||||||
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| 主題 | nonlinear resonance | |||||||||||||||||
| キーワード | ||||||||||||||||||
| 主題 | Duffing equation | |||||||||||||||||
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| 主題 | devil’s staircase | |||||||||||||||||
| キーワード | ||||||||||||||||||
| 主題 | chaos | |||||||||||||||||
| 書誌情報 |
en : Chaos, Solitons & Fractals 巻 111, p. 75-85, 発行日 2018-04-14 |
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| 収録物識別子タイプ | ISSN | |||||||||||||||||
| 収録物識別子 | 09600779 | |||||||||||||||||
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| 収録物識別子タイプ | NCID | |||||||||||||||||
| 収録物識別子 | AA10824244 | |||||||||||||||||
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| 収録物識別子タイプ | NCID | |||||||||||||||||
| 収録物識別子 | AA11523345 | |||||||||||||||||
| 出版者 | ||||||||||||||||||
| 出版者 | Elsevier | |||||||||||||||||
| 権利情報 | ||||||||||||||||||
| 権利情報 | © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ | |||||||||||||||||
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| 識別子 | 337485 | |||||||||||||||||
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| 言語 | eng | |||||||||||||||||
