Calculation Method of Local Bifurcation Point in Piecewise Nonlinear Discrete-Time Dynamical Systems
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- Tone Yusuke
- Faculty of Engineering, Oita University
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- Asahara Hiroyuki
- Faculty of Engineering, Fukuoka University
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- Ito Daisuke
- Faculty of Engineering, the University of Tokushima
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- Ueta Tetsushi
- Center for Administration of Information Technology, the University of Tokushima
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- Aihara Kazuyuki
- Institute of Industrial Science, the University of Tokyo
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- Kousaka Takuji
- Faculty of Engineering, Oita University
Bibliographic Information
- Other Title
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- 区分非線形離散時間力学系における局所的分岐点の計算法
- クブン ヒセンケイ リサン ジカン リキガクケイ ニ オケル キョクショテキ ブンキテン ノ ケイサンホウ
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Abstract
This paper proposes a calculation method of local bifurcation points for discrete-time dynamical systems with piecewise nonlinear characteristic (PNDDS). First, an n-dimensional PNDDS, which has two piecewise nonlinear maps, is shown and its variational equation is derived. Next, the calculation method of the local bifurcation points which utilizes the conditional equation of the periodic solution and the characteristic equation is proposed. Then, we have to calculate derivatives of the map with an initial value and with a bifurcation parameter to obtain the bifurcation points continuously in the parameter space. The above calculation process is a key of the proposed method, and we explain it in detail. Finally, we apply the proposed method to a two-dimensional PNDDS and calculate the local bifurcation points for confirming its validity.
Journal
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- IEEJ Transactions on Electronics, Information and Systems
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IEEJ Transactions on Electronics, Information and Systems 134 (5), 729-736, 2014
The Institute of Electrical Engineers of Japan
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Details 詳細情報について
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- CRID
- 1390001204608142080
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- NII Article ID
- 130004870044
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- NII Book ID
- AN10065950
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- ISSN
- 13488155
- 03854221
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- NDL BIB ID
- 025529375
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- Text Lang
- ja
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- Data Source
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- JaLC
- NDL
- Crossref
- CiNii Articles
- KAKEN
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- Abstract License Flag
- Disallowed