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 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v1 Introduction 12 The corresponding graph theory of an ODE system 23 Loop-searching systems 174 Robust Circadian Timekeeping 235 Appendix 28
 [1] Atsushi Mochizuki, Bernold Fiedler, Gen Kurosawa andDaisuke Saito. Dynamics and control at feedback vertexsets. I:Informative and determing nodes in regulatory networks(2013)[2] Atsushi Mochizuki, Bernold Fiedle, Gen Kurosawa andDaisuke Saito. Dynamics and control at feedback vertex sets.II:A faithful monitor to determine the diversity of molecularactivities in regulatory networks.(2013)[3] Jack K.Hale. Asymptotic behavior of dissipative systems(1988)[4] Kei-Ichi Ueda. Three-state network design for robust loopsearchingsystems(2013)[5] Kei-Ichi Ueda, Masaaki Yadome and Yasumasa Nishiura.Multistate network for loop searching with self-recoveryproperty(2014)[6] Horacio G. Rotstein, Nancy Kopell, Anatol M. Zhabotinskyand Irving R. Epstein. A canard mechanism for localizationin 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 robustcircadian timekeeping via stoichiometric balance(2012)[9] Jae Kyoung Kim, Zachary P. Kilpatrick, Matthew R. Bennett,Kre simir Josi c. Molecular mechanisms that regulate thecoupled 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 biochemicalfeedback control-I. the role of cooperativity andsaturability(1991)[12] Michael A. Schwemmer and Timothy J. Lewis. The Theoryof Weakly Coupled Oscillators.(2012)
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