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ID 116702
Author
Miino, Yuu Tokyo University of Technology
Keywords
homoclinic bifurcation
logistic map
global bifurcation
Feigenbaum constants
Content Type
Journal Article
Description
In this study, we have developed the method to obtain the homoclinic bifurcation parameter of an arbitrary targeted fixed point in the logistic map Tr. We have considered the geometrical structure of Tr around x =0.5 and derived the core condition of the bifurcation occurrence. As the result of numerical experiment, we have calculated the exact bifurcation parameter of the fixed point of Trℓ with ℓ≤256. We have also discussed the Feigenbaum constants found in the bifurcation parameter and the fixed point coordinate sequences. This fact implies the local stability of the fixed point and global structure around it are in association via the constants.
Journal Title
Nonlinear Theory and Its Applications, IEICE
ISSN
21854106
Publisher
The Institute of Electronics, Information and Communication Engineers
Volume
13
Issue
2
Start Page
209
End Page
214
Published Date
2022-04-01
Rights
©IEICE 2022
EDB ID
DOI (Published Version)
URL ( Publisher's Version )
FullText File
language
eng
TextVersion
Publisher
departments
Center for Administration of Information Technology