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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/44868完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 夏俊雄(Chun-Hiung Hsia) | |
| dc.contributor.author | Che-Wei Wu | en |
| dc.contributor.author | 吳哲瑋 | zh_TW |
| dc.date.accessioned | 2021-06-15T03:56:54Z | - |
| dc.date.available | 2015-06-20 | |
| dc.date.copyright | 2010-06-20 | |
| dc.date.issued | 2010 | |
| dc.date.submitted | 2010-06-18 | |
| dc.identifier.citation | [1]J. Evans and N. Shenk, Solutions to axon equations, Biophys. J. 10 (1970), 1090-1101
[2]E. Coddington and N. Levinson, Theory of Ordinary Differential Equations, McGraw Hill Book Company, Inc., New York, 1955. [3]J. Evans, Nerve Axon Equations: I linear approximations, Indiana Univ. Math. J. 21 (1972), 877-886 [4]J. Evans, Nerve Axon Equations: II stability at rest, Indiana Univ. Math. J. 22 (1972), 75-90 [5]M. W. Green and B. D. Sleeman, On Fitzhugh's nerve axon equations, Biology. J. 1 (1974) 152-163 [6]B. D. Sleeman, FitzHugh's nerve axon equations, Biology J. 2 (1975) 341-349 [7]R. FitzHugh, Impulses and physiological states in theoretical models of nerve membrane, Biophys. J. 1 (1961), 445-466. [8]R. FitzHugh, Mathematical models of excitation and propagation on nerve, Chapter 1, pages 1-85 of Biological Engineering, H. P. Schwan Ed., McGraw Hill Book Company, Inc., New York, 1969. [9]R. FitzHugh and H. A. Antosiewicz, Automatic computation of nerve excitation, detailed corrections and additions, J. Soc. Ind. Appl. Math. 7 (1959), 447-458 [10]J. Nagumo, S. Arimoto and S. Yoshizawa, An active pulse transmission line simulating nerve axon, Proc. IRE 50 (1962), 2061-2070. [11]J. Z. Hearon, Application of results from linear kinetics to the Hodgkin-Huxley equations}, Biophys. J. 4 (1964), 69-75 | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/44868 | - |
| dc.description.abstract | 這篇論文統整了四篇文章，分別是參考文獻中的第三、四、五、六篇。
在第一章節中，我們統整FitzHugh所提出一般方程解的指數穩定性。對解做小擾動後，原本方程的指數穩定性可以由對應的線性化方程所決定。 在第二章節中，我們探討線性化方程和傅立葉轉換方程靜止指數穩定性的關係，其中這個矩陣[c d;e A]的特徵值和靜止指數穩定性有相關連。 在第三章節中，放了FitzHugh方程指數穩定性的證明及其傳動波波速的上、 下界。 | zh_TW |
| dc.description.abstract | In this article, we survey the exponential stability of the nerve axon equations form Evans [3, 4], Sleeman [6], and Green and Sleeman [5].
In Section 1, we survey the stability of solution to the general system given by FitzHugh. Under small perturbations of a solution , the system can be characterized by the stability properties of the corresponding linearized system. In Section 2, we explore the relation of the stability of the linearized system and the Fourier transform system. One can achieve a characterization of the stability at rest in terms of properties of the matrix [c d;e A]. The proof of the exponential stability of FitzHugh's system and the characterization of the wave speed of the travelling wave solutions are put in Section 3. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-15T03:56:54Z (GMT). No. of bitstreams: 1 ntu-99-R97221003-1.pdf: 414754 bytes, checksum: 1daa8c11cfd65e9d247ac1423075493d (MD5) Previous issue date: 2010 | en |
| dc.description.tableofcontents | 摘要.......................................ii
Abstract...................................iii 1 Linear Approximations 1 1.1 Introduction.........................1 1.2 Definitions..........................2 1.3 Main Result..........................2 1.4 Proof of the Theorem.................3 2 Stability at Rest 8 2.1 Introduction.........................8 2.2 Main Result..........................8 2.3 Proof of the Theorem.................9 3 FitzHugh’s Nerve Axon Equations 20 3.1 Introduction........................20 3.2 Exponential Stability at Rest.......21 3.3 A Lower Bound for the Wave Speed c..23 3.4 An Upper Bound for the Wave Speed c.24 References................................27 | |
| dc.language.iso | en | |
| dc.subject | 指數穩定性 | zh_TW |
| dc.subject | exponential stability | en |
| dc.title | 神經軸突方程的指數穩定性 | zh_TW |
| dc.title | The Exponential Stability of the Nerve Axon Equations | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 98-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | Hongqiu Chen(Hongqiu Chen),Jerry Bona(Jerry Bona) | |
| dc.subject.keyword | 指數穩定性, | zh_TW |
| dc.subject.keyword | exponential stability, | en |
| dc.relation.page | 28 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2010-06-18 | |
| 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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