ID 111897
著者
Miino, Yuu Tokushima University
キーワード
bifurcation analysis
hybrid system
nonlinear resonance
Duffing equation
devil’s staircase
chaos
資料タイプ
学術雑誌論文
抄録
The Duffing equation describes a periodically forced oscillator model with a nonlinear elasticity. In its circuitry, a saturable-iron core often exhibits a hysteresis, however, a few studies about the Duffing equation has discussed the effects of the hysteresis because of difficulties in their mathematical treatment. In this paper, we investigate a forced planer system obtained by replacing a cubic term in the Duffing equation with a hysteresis function. For simplicity, we approximate the hysteresis to a piecewise linear function. Since the solutions are expressed by combinations of some dynamical systems and switching conditions, a finite-state machine is derived from the hybrid system approach, and then bifurcation theory can be applied to it. We topologically classify periodic solutions and compute local and grazing bifurcation sets accurately. In comparison with the Duffing equation, we discuss the effects caused by the hysteresis, such as the devil’s staircase in resonant solutions.
掲載誌名
Chaos, Solitons & Fractals
ISSN
09600779
cat書誌ID
AA10824244
AA11523345
出版者
Elsevier
111
開始ページ
75
終了ページ
85
発行日
2018-04-14
備考
本文は2020-04-14以降公開予定
権利情報
© 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
EDB ID
出版社版DOI
出版社版URL
言語
eng
著者版フラグ
その他
部局
情報センター
理工学系