著作: [稲葉 直彦]/Tadashi Tsubone/Hidetaka Ito/Hideaki Okazaki/[吉永 哲哉]/Nested mixed-mode oscillations, Part III: Comparison of bifurcation structures between a driven Bonhoeffer-van der Pol oscillator and Nagumo-Sato piecewise-linear discontinuous one-dimensional map/[Physica D: Nonlinear Phenomena]
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種別 | 必須 | 学術論文(審査論文) | |||
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言語 | 必須 | 英語 | |||
招待 | 推奨 | ||||
審査 | 推奨 | Peer Review | |||
カテゴリ | 推奨 | 研究 | |||
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題名 | 必須 |
(英) Nested mixed-mode oscillations, Part III: Comparison of bifurcation structures between a driven Bonhoeffer-van der Pol oscillator and Nagumo-Sato piecewise-linear discontinuous one-dimensional map |
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副題 | 任意 | ||||
要約 | 任意 |
(英) In our previous studies (Inaba and Kosaka, (2020); Inaba and Tsubone, (2020)), we discovered bifurcation structures represented by nested mixed-mode oscillations (MMOs) generated by a driven Bonhoeffer-van der Pol (BVP) oscillator. BVP oscillators are equivalent to FitzHugh Nagumo models and have been a subject of intense research for the last six decades. In this study, we consider the case in which the diode included in a driven BVP oscillator is assumed to operate as an ideal switch. In this case, Poincaré return maps can be rigorously constructed one-dimensionally, which consist of two downward convex branches. We also consider the Poincaré return map that is approximated as a two-segment piecewise-linear discontinuous one-dimensional map. Such a piecewise-linear map was proposed by Nagumo and Sato and generates nested period-adding bifurcations. We show that the possible solutions of un-nested, singly, and doubly nested period-adding bifurcations generated by the Nagumo-Sato map coincide with those of un-nested, singly, and doubly nested MMO-incrementing bifurcations, respectively, generated with the BVP oscillator. |
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キーワード | 推奨 | ||||
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誌名 | 必須 |
Physica D: Nonlinear Phenomena([Elsevier Science B.V.])
(pISSN: 0167-2789)
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巻 | 必須 | 446 | |||
号 | 必須 | --- | |||
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年月日 | 必須 | 2023年 1月 26日 | |||
URL | 任意 | https://www.sciencedirect.com/science/article/pii/S0167278923000210 | |||
DOI | 任意 | 10.1016/j.physd.2023.133667 (→Scopusで検索) | |||
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指導教員 | 推奨 | ||||
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