ID 111897
Author
Miino, Yuu Tokushima University
Keywords
bifurcation analysis
hybrid system
nonlinear resonance
Duffing equation
devil’s staircase
chaos
Content Type
Journal Article
Description
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.
Journal Title
Chaos, Solitons & Fractals
ISSN
09600779
NCID
AA10824244
AA11523345
Publisher
Elsevier
Volume
111
Start Page
75
End Page
85
Published Date
2018-04-14
Remark
本文は2020-04-14以降公開予定
Rights
© 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
337485
DOI (Published Version)
URL ( Publisher's Version )
language
eng
TextVersion
その他
departments
Center for Administration of Information Technology
Science and Technology