具有反馈控制的Logistic和Richards模型的定性分析  

Qualitative Analysis to Logistic and Richards Models with Feedback Controls

作　　者：胡宝安[1] 李亚玲[1] 刘俊[1] 

机构地区：[1]军事交通学院基础部,天津300161

出　　处：《军事交通学院学报》2012年第8期89-91,共3页Journal of Military Transportation University

摘　　要：对具有反馈控制的广义Logistic和Richars模型进行定性分析。分析了平衡点的局部稳定性，用Dulac判据法证明了系统不存在极限环，进一步证明了系统唯一的正平衡点是全局渐近稳定的。通过引入反馈控制量，使得系统的平衡态小于环境容纳量，从而避免了以往模型的不足。In this paper, the Logistic and Richards models with feedback controls were investigated. This paper analyzed lo- cal stability of the equilibriums. By using Dulac function, proved that the system didn＇ t exist limit - cycles. It shows that the positive equilibrium of system, which is smaller than capacity of environment, is globally asymptotically stable.

关 键 词：反馈控制 极限环 全局渐近稳定 

分 类 号：O175.14[理学—数学]