The Monotone Theory And The Circadian Oscillation Model

In the past few decades, the science of biology had developed very fast, especially the system biology. The characteristics of system biology were researched by not only the biologists, but also the mathematicians and physical scientists, such as robust, auto adjustability and so on. The circadian oscillation is one main aspect of system biology, the research of circadian oscillation include the analysis of stability and the factors which affect the circadian oscillation. This paper mainly studies the foundation of the models, the analysis of stability and the factors which affect the circadian oscillation.(1)The foundation of the circadian oscillation models, which was based on the negative feedback theory and Goodwin model. Firstly, the negative feedback in the circadian oscillation was introduced, with the analysis of the circadian oscillation, the negative feedback existed in most circadian oscillation models was found, and the negative feedback guaranteed the oscillation exist in most organisms. Secondly, with the analysis of the Goodwin model, the conditions of oscillation were proposed , with the analysis of neurospora circadian oscillation model based on the Routh criterion, the condition of Hopf bifurcation was got.(2)The stability analyze of circadian oscillation. Firstly, the ten dimensions drosophila model stability was analyzed by the small-gain theory, with the linear method and numerical analysis, the condition and the scan of when the complicated drosophila system stable was concluded. With the parameters of the system, the conditions of when the system oscillation were calculated. Secondly, when the ten drosophila model is dissymmetry about the per and tim sub-system, the chaos state might appear at the complicated system for the complicated dynamic characters under dissymmetry state.(3)The L-D cycle affect to the drosophila model. When the system is add the L-D cycle, the oscillation conditions of the drosophila model will alter. With the affection of L-D cycle, the circadian oscillation will get a special synchronization—phase synchronization. When the system under condition of chaos, if the L-D control is add into the system and the strength is big enough, the system will deviate from the state of chaos and get into the state of circadian oscillation.The proposed numerical simulations verify the corresponding theoretical results; especially indicate that the period of circadian oscillation was 24 hours.