改进的口腔微生物种群模型及其Lyapunov稳定性  

Improved Oral Chemostat Models and Their Lyapunov Stability

作　　者：杨坤一[1] 信鸽 杨星亚[2] 

机构地区：[1]北方工业大学理学院,北京100144 [2]合肥工业大学(新区)经济学院,安徽合肥230031

出　　处：《数学的实践与认识》2012年第23期157-163,共7页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11126138)

摘　　要：考察人体口腔异味现象,利用恒化器建模方法,改进了人体口腔系统中微生物种群关系的模型,利用Lyapunov稳定性理论分析了系统的平衡点及其稳定性.进而得到结论,口腔异味作为疾病,需要专业医治才能治愈.数值模拟结果证实了理论分析的正确性.In this paper, we consider phenomenon of oral oder. Firstly, after the assumption of ration-dependent increasing rate function, we set up the ordinary differential equations models for the relations between human oral microorganism populations. They are chemostat models that have been widely applied in both mathematical and biological fields. Secondly, using the Lyapunov stability theory, we analyze asymptotic behavior for solutions of differential equations＇ models and get the stability results for the balance nodes. Then we have the main result.- bad breath, as a disease, should be cured by professional methods. Simulation results prove our results.

关 键 词：口腔异味 恒化器模型 微分方程 LYAPUNOV稳定性理论 

分 类 号：O175[理学—数学]