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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/8604完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 夏俊雄(Chun-Hsiung Hsia) | |
| dc.contributor.author | Chung-Lin Tseng | en |
| dc.contributor.author | 曾仲麟 | zh_TW |
| dc.date.accessioned | 2021-05-20T19:58:51Z | - |
| dc.date.available | 2010-07-12 | |
| dc.date.available | 2021-05-20T19:58:51Z | - |
| dc.date.copyright | 2010-07-12 | |
| dc.date.issued | 2010 | |
| dc.date.submitted | 2010-07-06 | |
| dc.identifier.citation | [1] Arnol’d, V. I. “Supplementary Chapter of the Theory of Ordinary Differential Equations”, Nauka, Moscow (1978), 304 pp. (in Russian)
[2] Coddington, E. A. and Levinson, N. “Theory of Ordinary Differential Equations”, McGraw-Hill, N. Y. (1955) 429 pp [3] Crandall, M. G. and Rabinowitz, P. H. Bifurcation from simple eigenvalues, J. Funct. Anal.8 (1971), 321-340 [4] Hale, J. K. “Ordinary Differential Equations”, Applied Math. Sci. vol. 3, Springer-Verlag, N. Y. (1971) [5] Hassard, B. D., Kazarinoff, N. D. and Wan Y.-H. Theory and Applications of Hopf Bifurcation, Cambridge Univ. Press, Cambridge (1981) [6] Hartman, P. “Ordinary Differential Equations”, Second Edition, P. Hartman (1973) [7] Kelly, A. The stable, center-stable, center, center-unstable, and stable manifolds, J. Diff. Eqns. 3 (1967), 546-570 [8] Poore, A. B. On the theory and application of the Hopf-Friedrichs bifurcation theory, Arch. Rat. Mech. and Anal. 60 (1975-76), 371-393 | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/8604 | - |
| dc.description.abstract | This paper is a survey on Hopf bifurcation, Hopf bifurcation is very important in many areas. In this paper, we focus on the properties and proofs of Hopf bifurcation. The proof in this paper give the bifurcation formula, and we give some examples after we proved the theorem. | en |
| dc.description.provenance | Made available in DSpace on 2021-05-20T19:58:51Z (GMT). No. of bitstreams: 1 ntu-99-R97221030-1.pdf: 311020 bytes, checksum: 95f7047bb27a5dea9cc237ef02aab84e (MD5) Previous issue date: 2010 | en |
| dc.description.tableofcontents | 誌謝………………………………………………………………… i
中文摘要…………………………………………………………… ii 英文摘要…………………………………………………………… iii 1.Introduction …………………………………………………… 1 2.Statement of the Theorem …………………………………… 1 3.Proof of the Theorem ………………………………………… 3 3.1Part 1(A) Existence ………………………………………… 3 3.2Part 1(B) Bifurcation Formula …………………………… 5 3.3Part 1(C) Stability ………………………………………… 10 3.4Part 2 Reduction of Two-dimensional Systems to Poincar`e Normal Form ………………………………………………… 13 3.5 Part 3 Reduce the n-dimensional System to the Two-dimensional System by Center Manifold Theorem ……………… 16 4.Examples ………………………………………………………… 24 參考文獻…………………………………………………………… 28 | |
| dc.language.iso | en | |
| dc.subject | Hopf | en |
| dc.subject | bifurcation | en |
| dc.subject | Floquet theorem | en |
| dc.subject | center manifold | en |
| dc.subject | periodic solution | en |
| dc.title | Hopf 分歧之研究與探討 | zh_TW |
| dc.title | A Survey On Hopf bifurcation | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 98-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | Jerry Lloyd Bona(Jerry Lloyd Bona),Hongqiu Chen(Hongqiu Chen) | |
| dc.subject.keyword | Hopf,分歧,Floquet定理,週期解,中央流型, | zh_TW |
| dc.subject.keyword | Hopf,bifurcation,Floquet theorem,center manifold,periodic solution, | en |
| dc.relation.page | 29 | |
| dc.rights.note | 同意授權(全球公開) | |
| dc.date.accepted | 2010-07-06 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| 顯示於系所單位： | 數學系 | |
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