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language
eng
Author
Ishibashi, Kazuki Department of Electronic Control Engineering, National institute of Technology, Hiroshima College,
Description
As is well known, Mathieu’s equation is a representative of mathematical models describing
parametric excitation phenomena. This paper deals with the oscillation problem for
Mathieu’s equation with two frequencies. The ratio of these two frequencies is not necessarily
a rational number. When the ratio is an irrational number, the coefficient of Mathieu’s
equation is is quasi-periodic, but not periodic. For this reason, the basic knowledge
for linear periodic systems such as Floquet theory is not useful. Whether all solutions of
Mathieu’s equation oscillate or not is determined by parameters and frequencies. Our results
provide parametric conditions to guarantee that all solutions are nonoscillatory. The
advantage of the obtained parametric conditions is that it can be easily checked. Parametric
nonoscillation region is drawn to understand these results easily. Finally, several
simulations are carried out to clarify the remaining problems.
Subject
Nonoscillation
Parametric excitation
Mathieu’s equation
Frequencies
Quasi-periodic
Journal Title
Applied Mathematics and Computation
Volume
346
Start Page
491
End Page
499
ISSN
0096-3003
Published Date
2019-04
DOI
Publisher
Elsevier
NII Type
Journal Article
Format
PDF
Text Version
著者版
OAI-PMH Set
Department of Mathematics, Faculty of Science and Engineering
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