摘要 藍綠藻是擁有概日韻律現象的最低等生物，Kai蛋白質家族和此韻律高度相關。先前之研究者並發現，在試管中以三種Kai蛋白與ATP便能構築一個試管內的概日韻律震盪子，即Kai蛋白之磷酸態呈現近二十四小時週期之震盪。解析此現象的分子機制或許有助於理解各種生命現象的基本特質。本文介紹此系列相關之研究，並且以非線性動力學的觀點來分析一個描述此現象的數學模型。藉由觀察震盪的振幅及週期，我們發現，調動模型的某些參數時，震盪之出現與消失具有無限週期分岔或是霍普夫分岔的性質。另一角度，由模型得出特徵值的性質，亦可印證霍普夫分岔的發生。 Abstract Cyanobacteria is the simplest organism that perform the circadian rhythm. Kai protein family is highly related to this phenomenon. Researchers discovered that a in-vitro circadian rhythmic oscillator can be reconstituted with KaiA, KaiB, KaiC and ATP. That is, the phosphorylation state of KaiC performs 24 hours periodic oscillation. To unravel the molecular mechanism of this phenomenon may be helpful to understand the essential feature of life. In this thesis, we introduce some important research on this topic, and analyze a mathematical model describing the circadian rhythm from the viewpoint of nonlinear dynamics. We tuned the parameters, and observe the amplitude and period of the oscillation. We found, in some cases, the oscillation may emerge or disappear through a Hopf or infinite period bifurcation. And the evidence in the eigenvalues of the systems also support that Hopf bifurcation indeed happen.
