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.