神經軸突方程的指數穩定性

The Exponential Stability of the Nerve Axon Equations

吳哲瑋(Che-Wei Wu)

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.2010.01465

摘要

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。

關鍵字

指數穩定性

並列摘要

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.

並列關鍵字

exponential stability

參考文獻

[1]J. Evans and N. Shenk, Solutions to axon equations, Biophys. J. 10 (1970), 1090-1101

[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