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Mode Selection Rules and Bifurcation Diagrams for Two-Delay Systems: Underlying Mechanism Controlled by Embedded Multidimensional Maps
http://hdl.handle.net/10228/00007523
http://hdl.handle.net/10228/000075239e21b441-e53c-40b2-8b41-720ce2e0c445
| 名前 / ファイル | ライセンス | アクション |
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10333901.pdf (12.7 MB)
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| アイテムタイプ | 学術雑誌論文 = Journal Article(1) | |||||
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| 公開日 | 2020-01-10 | |||||
| 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 | |||||
| タイトル | ||||||
| タイトル | Mode Selection Rules and Bifurcation Diagrams for Two-Delay Systems: Underlying Mechanism Controlled by Embedded Multidimensional Maps | |||||
| 言語 | en | |||||
| 言語 | ||||||
| 言語 | eng | |||||
| 著者 |
高橋, 公也
× 高橋, 公也× Kobayashi, Taizo |
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| 抄録 | ||||||
| 内容記述タイプ | Abstract | |||||
| 内容記述 | We study mode selection rules at the first bifurcation and bifurcation diagrams for a two-delay system with a positive feedback of a long delay time t2 and with either a positive or negative feedback of a short delay time t1, i.e., 0 < t1 < t2. The mode excited by the first bifurcation changes with t1/t2, and the relevant and irrelevant conditions, which are rational numbers in t1/t2 with t1/t2 = n/m, characterize the mode selection rule; a definite subset of the rational numbers is relevant and its complement is irrelevant. In a neighborhood of a relevant condition, oscillations each with period T ≈ 2t2/m, i.e., mth-order harmonic, are excited at the first bifurcation. In a neighborhood of an irrelevant condition, twin peaks consisting of higher-order harmonics are observed. The mode selection rule markedly changes with the strength of the short delay; the relevant condition changes reflecting the change in the underlying mechanism of the bifurcation process. In this paper, we show that for each of the relevant and irrelevant conditions, the two-delay system is reduced to an m-dimensional map in the nondispersive limit, i.e., a singular perturbation limit. In terms of multidimensional maps, the first bifurcation for the relevant condition is either a pitchfork or period-doubling bifurcation, while a Hopf bifurcation is observed for the irrelevant condition. The mode selection rules together with the waveforms are explained from the analysis of the multidimensional maps. Furthermore, the global structure of transitions among attractors after the first bifurcation is approximately predicted from the analysis of the multidimensional maps. | |||||
| 書誌情報 |
Journal of the Physical Society of Japan 巻 88, 号 2, 発行日 2019-01-10 |
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| 出版社 | ||||||
| 出版者 | 日本物理学会 | |||||
| DOI | ||||||
| 関連タイプ | isVersionOf | |||||
| 識別子タイプ | DOI | |||||
| 関連識別子 | info:doi/10.7566/JPSJ.88.024002 | |||||
| NAID | ||||||
| 関連タイプ | isVersionOf | |||||
| 識別子タイプ | NAID | |||||
| 関連識別子 | 210000135086 | |||||
| 日本十進分類法 | ||||||
| 主題Scheme | NDC | |||||
| 主題 | 548 | |||||
| NCID | ||||||
| 収録物識別子タイプ | NCID | |||||
| 収録物識別子 | AA00704814 | |||||
| ISSN | ||||||
| 収録物識別子タイプ | EISSN | |||||
| 収録物識別子 | 1347-4073 | |||||
| ISSN | ||||||
| 収録物識別子タイプ | PISSN | |||||
| 収録物識別子 | 0031-9015 | |||||
| 著作権関連情報 | ||||||
| 権利情報 | Copyright (c) 2019 The Physical Society of Japan | |||||
| 出版タイプ | ||||||
| 出版タイプ | AM | |||||
| 出版タイプResource | http://purl.org/coar/version/c_ab4af688f83e57aa | |||||
| 査読の有無 | ||||||
| 値 | yes | |||||
| 研究者情報 | ||||||
| URL | https://hyokadb02.jimu.kyutech.ac.jp/html/250_ja.html | |||||
| 論文ID（連携） | ||||||
| 値 | 10333901 | |||||
| 連携ID | ||||||
| 値 | 7510 | |||||
| 情報源 | ||||||
| 識別子タイプ | DOI | |||||
| 関連識別子 | https://doi.org/10.7566/JPSJ.88.024002 | |||||
| 関連名称 | https://doi.org/10.7566/JPSJ.88.024002 | |||||
