徳島大学 教育・研究者情報データベース(EDB)

1. 徳島大学.大学院医歯薬学研究部.保健学域.保健科学部門.放射線科学系.医用画像機器工学(2015年4月1日〜)

1. 稲葉 直彦(明治大学/宇都宮大学)

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2. (英) Sekikawa, Munehisa / (日) 関川, 宗久 / (読) せきかわ むねひさ

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3. (英) Shinotsuka, Yoshimasa / (読) しのつか よしまさ

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4. (英) Kamiyama, Kyohei / (読) かみやま きょうへい

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5. 藤本 憲市

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6. 吉永 哲哉([徳島大学.大学院医歯薬学研究部.保健学域.保健科学部門.放射線科学系.医用画像機器工学])

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7. (英) Endo, Tetsuro / (日) 遠藤, 哲郎 / (読) えんどう てつろう

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(英) Bifurcation scenarios for a 3D torus and torus-doubling

(英) Bifurcation transitions between a 1D invariant closed curve (ICC), corresponding to a 2D torus in vector fields, and a 2D invariant torus (IT), corresponding to a 3D torus in vector fields, have been the subjects of intensive research in recent years. An existing hypothesis involves the bifurcation boundary between a region generating an ICC and a region generating an IT. It asserts that an IT would be generated from a stable fixed point as a consequence of two Hopf (or two Neimark Sacker) bifurcations. We assume that this hypothesis may puzzle many researchers because it is difficult to assess its validity, although it seems to be a reasonable bifurcation scenario at first glance. To verify this hypothesis, we conduct a detailed Lyapunov analysis for a coupled delayed logistic map that can generate an IT, and indicate that this hypothesis does not hold according to numerical results. Furthermore, we show that a saddle-node bifurcation of unstable periodic points does not coincide with the bifurcation boundary between an ICC and an IT. In addition, the bifurcation boundaries of torus doubling do not coincide with a period-doubling bifurcation of unstable periodic points. To conclude, torus bifurcations have no relation with the bifurcations of unstable periodic points. Additionally, we exactly derive a quasi-periodic Hopf bifurcation boundary introducing a double Poincaré map.