摘要
本篇論文主要是在探討一個連續攪動的槽反應器模型之實分歧及Hopf分歧問題。我們使用Hopf分歧定理及牛頓迭代法,來求模型平衡解路徑上的Hopf分歧點及實分歧點,亦使用切線預測法﹑割線預測法﹑牛頓迭代法﹑隱函數定理﹑虛擬弧長延拓法,找出過實分歧點的平衡解路徑,並使用打靶法﹑切線預測法﹑Runge-Kutta法﹑割線預測法﹑牛頓迭代法﹑隱函數定理及虛擬弧長延拓法,求出過Hopf分歧點的週期解路徑。

Abstract
The main purpose of this paper is to study the numerical investigation for the real and Hopf bifurcation problems of a Continuous Stirred Tank Reactor model. We use the Hopf bifurcation theorem and Newton’s method to compute Hopf bifurcation points and real bifurcation points. We use the tangent predictor, secant predictor, Newton’s method, implicit function theorem and the pseudo-arclength continuation method to follow the steady-state solution branches which passes through a real bifurcation point, we also use the shooting method, Runge-Kutta method, tangent predictor, secant predictor, Newton’s method, implicit function theorem, and the pseudo-arclength continuation method to follow the periodic solution branches which passes through a Hopf bifurcation point.

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