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一个时滞微生物增长模型全局动力学性态的Lyapunov函数法

The Global Dynamics of a Delayed Microbial Growth Model for Lyapunov Functions
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摘要 利用Lyapunov函数和LaSalle不变原理研究了一个时滞微生物增长模型的全局动力学性态,证明了微生物灭绝平衡点和持续生存平衡点的全局渐近稳定性,简化了现有研究方法,并将结论从已有文献中仅适用于微生物营养利用的Michaelis-Menten功能反应函数加强到适用于一般功能反应函数. In this paper,the global dynamics of a delayed microbial growth model is studied by using the Lyapunov function and the LaSalle-type theorem,and the global asymptotical stabilities of the microbial extinction equilibrium and the microbial survival equilibrium are obtained.The proofs in related literature are simplified and the conclusions are improved so that they are applicable not only for the Michaelis-Menten functional response of microbial nutrient utilization as in previous studies,but also for general functional responses.
作者 吴凡 刘贤宁 李鸣明
机构地区 西南大学数学与统计学院
出处 《西南大学学报（自然科学版）》 CAS CSCD 北大核心 2014年第5期67-71,共5页 Journal of Southwest University(Natural Science Edition)
基金 国家自然科学基金资助项目(11271303)
关键词 时滞 LYAPUNOV函数 LaSalle不变原理 局部稳定性 全局稳定性 delay Lyapunov function LaSalle-type invariance theorem local stability global stability
分类号 O175.13 [理学—基础数学]
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参考文献16

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二级参考文献8

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西南大学学报（自然科学版）
2014年 第5期

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