一类竞争的病菌传染模型的稳定性  

A type of rival germ infects the stability of pattern

作　　者：左晓虹[1] 

机构地区：[1]三门峡职业技术学院公共教学部,河南三门峡472000

出　　处：《三门峡职业技术学院学报》2017年第1期140-144,共5页Journal of Sanmenxia Polytechnic

基　　金：三门峡职业技术学院科研项目(SZY-2016-002)

摘　　要：生物数学是在生物学的不同领域中应用数学工具对生命现象进行研究的一门交叉学科,该门学科研究生物种群体与环境之间、生物群体之间的关系,这种关系常常需要建立相应的微分方程模型,将一个复杂的生物学问题借助数学模型转变成一个数学问题,通过对数学模型的求解,可获得生物现象的相关结论,从而达到对生命现象进行研究的目的,实现对某些生态问题的预测。本文研究了一类竞争的病菌传染模型,并对该模型的一致持久性和有界性及正平衡态的存在性进行了探讨,并列举实例对结论进行了验证。Mathematical biology is an interdisciplinary subject, which applies mathematical tool to study biological phenomena in different fields of Biology.The relationships between the species groups and the environment and between the biological communities are researched in this subject. By establishing Corresponding differential equation models, complex biological problems are transformed into mathematical problems with the aid of mathematical models.By solving the mathematical model, the related conclusions of biological phenomena can be obtained. Furthermore, we achieve the purpose of the study of the phenomenon of life and realize the prediction of some ecological problems. In this paper, we study a class of competitive pathogen infection model, and discuss the uniform persistence and boundedness of the model and the local asymptotic stability of the solution of the model when and are small enough in the model.

关 键 词：微分方程 生态模型 稳定性 平衡点 

分 类 号：O175[理学—数学]