Hopf 分歧之研究與探討

A Survey On Hopf bifurcation

曾仲麟(Chung-Lin Tseng)

指導教授 ： 夏俊雄

國立臺灣大學/理學院/數學研究所/碩士(2010年)

https://doi.org/10.6342/NTU.2010.00031

摘要

無資料

關鍵字

Hopf ； 分歧 ； Floquet定理 ； 週期解 ； 中央流型

並列摘要

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.

並列關鍵字

Hopf ； bifurcation ； Floquet theorem ； center manifold ； periodic solution

參考文獻

[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)

[6] Hartman, P. “Ordinary Differential Equations”, Second Edition, P. Hartman (1973)