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ID 114909
Author
Miino, Yuu Tokyo University of Technology
Keywords
local and global bifurcation analysis
piecewise linear dynamical system
hybrid dynamical system
Duffing equation
Content Type
Journal Article
Description
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.
Journal Title
Nonlinear Theory and Its Applications, IEICE
ISSN
21854106
Publisher
The Institute of Electronics, Information and Communication Engineers
Volume
11
Issue
3
Start Page
359
End Page
371
Published Date
2020-07-01
Rights
© IEICE 2020
EDB ID
DOI (Published Version)
URL ( Publisher's Version )
FullText File
language
eng
TextVersion
Publisher
departments
Center for Administration of Information Technology
Science and Technology