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研究生:呂懷華
研究生(外文):Huai-hua Lu
論文名稱:一階微分方程與生物網格系統
論文名稱(外文):First order differential equations and biology network systems
指導教授:陳俊全陳俊全引用關係
口試委員:林太家夏俊雄
口試日期:2015-06-11
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:數學研究所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2015
畢業學年度:103
語文別:英文
論文頁數:32
中文關鍵詞:網格系統
外文關鍵詞:network systems
相關次數:
  • 被引用被引用:0
  • 點閱點閱:188
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  • 收藏至我的研究室書目清單書目收藏:0
在許多生物化學系統中,常微分方程往往可給出這些系統的特性
,然而一般方程解的行為並不容易刻畫,在這篇文章中我們介紹
從圖論衍生出的工具來對應方程系統,並且介紹以生物上既有的
現象來建立兩種數學模型,進而表現出這些生物特性,而我的工
作在section 2的定理2.10和2.11,是由Fiedler, Mochizuki, Kurosawa, Saito,2013的定理衍生而來,可將常微分方程簡化為子系統
,行為較整體容易掌握。

In biology and chemistry, ODE system is a good way to represent some of their special properties. In this article we mention about some tools from graph theory to deal with ODE systems and two models designed to fulfill some biological properties. My results are Theorem 2.10 and Theorem 2.11 in section 2 coming from the ideas in (Fiedler, Mochizuki, Kurosawa, Saito,2013). The Theorems can reduce an ODE system to subsystems which makes a system easy to analyze.

目錄Contents
口試委員審定書i
中文摘要ii
英文摘要iii
圖目錄v
1 Introduction 1
2 The corresponding graph theory of an ODE system 2
3 Loop-searching systems 17
4 Robust Circadian Timekeeping 23
5 Appendix 28

[1] Atsushi Mochizuki, Bernold Fiedler, Gen Kurosawa and
Daisuke Saito. Dynamics and control at feedback vertex
sets. I:Informative and determing nodes in regulatory networks(
2013)
[2] Atsushi Mochizuki, Bernold Fiedle, Gen Kurosawa and
Daisuke Saito. Dynamics and control at feedback vertex sets.
II:A faithful monitor to determine the diversity of molecular
activities in regulatory networks.(2013)
[3] Jack K.Hale. Asymptotic behavior of dissipative systems(
1988)
[4] Kei-Ichi Ueda. Three-state network design for robust loopsearching
systems(2013)
[5] Kei-Ichi Ueda, Masaaki Yadome and Yasumasa Nishiura.
Multistate network for loop searching with self-recovery
property(2014)
[6] Horacio G. Rotstein, Nancy Kopell, Anatol M. Zhabotinsky
and Irving R. Epstein. A canard mechanism for localization
in systems of globally coupled oscillators.(2003)
[7] Brian Ingalls. Mathematical Modelling in Systems Biology:
An Introduction.(2012)
[8] Jae Kyoung Kim and Daniel B Forger. A mechanism for robust
circadian timekeeping via stoichiometric balance(2012)
[9] Jae Kyoung Kim, Zachary P. Kilpatrick, Matthew R. Bennett,
Kre simir Josi c. Molecular mechanisms that regulate the
coupled period of the mammalian circadian clock
[10] Daniel B. Forger. Signal processing in cellular clocks.(2010)
[11] C. D. Thron. The secant condition for instability in biochemical
feedback control-I. the role of cooperativity and
saturability(1991)
[12] Michael A. Schwemmer and Timothy J. Lewis. The Theory
of Weakly Coupled Oscillators.(2012)

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