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ID 114909
著者
美井野, 優 Tokyo University of Technology
キーワード
local and global bifurcation analysis
piecewise linear dynamical system
hybrid dynamical system
Duffing equation
資料タイプ
学術雑誌論文
抄録
We replace the cubic characteristics in the Duffing equation by two line segments connected at a point and investigate how an angle of that broken line conducts bifurcations to periodic orbits. Firstly we discuss differences in periodic orbits between the Duffing equation and a forced planar system including the broken line. In the latter system, a grazing bifurcation split the parameter space into the linear and nonlinear response domains. Also, we show that bifurcations of non-resonant periodic orbits appeared in the former system are suppressed in the latter system. Secondly, we obtain bifurcation diagrams by changing a slant parameter of the broken line. We also find the parameter set that a homoclinic bifurcation arises and the corresponding horseshoe map. It is clarified that a grazing bifurcation and tangent bifurcations form boundaries between linear and nonlinear responses. Finally, we explore the piecewise linear functions that show the minimum bending angles exhibiting bifurcation and chaos.
掲載誌名
Nonlinear Theory and Its Applications, IEICE
ISSN
21854106
出版者
The Institute of Electronics, Information and Communication Engineers
11
3
開始ページ
359
終了ページ
371
発行日
2020-07-01
権利情報
© IEICE 2020
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出版社版DOI
出版社版URL
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言語
eng
著者版フラグ
出版社版
部局
情報センター
理工学系