一階微分方程與生物網格系統

Abstract

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.