具有时滞及B-D功能反应的食物链系统周期解的存在性与全局渐近稳定性

熊友兵;李红智

系统科学与数学 ›› 2008, Vol. 28 ›› Issue (3) : 288-301.

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PDF(392 KB)
系统科学与数学 ›› 2008, Vol. 28 ›› Issue (3) : 288-301. DOI: 10.12341/jssms10069
论文

具有时滞及B-D功能反应的食物链系统周期解的存在性与全局渐近稳定性

    熊友兵(1),李红智(2)
作者信息 +

Existence and Global Asymptotic Stability of Periodic Solution in a Food-Chain System with Delays and Beddington-Deangelis Functional Response

    XIONG Youbing(1),LI Hongzhi(2)
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文章历史 +

摘要

研究了具有时滞和Beddington-DeAngelis功能反应的一类食物链系统,通过运用Mawhin重合度理论中的延拓定理,得到了系统至少存在一个周期解的充分条件,并通过构造Lyapunov泛函的方法得到了系统周期解的全局稳定性.

Abstract

A delayed three-species food-chain model with Beddington-DeAngelis functional
response is investigated. By using Gaines and Mawhin's continuation theorem of
coincidence degree theory, sufficient conditions are obtained for the existence
of positive periodic solutions to the proposed model. By constructing a suitable
Lyapunov functional, the global asymptotic stability of the periodic solutions is established.

关键词

时滞 / 功能反应 / 周期解 / 重合度 / 全局稳定性.

Key words

Time delay / functional response / periodic solution / coincidence degree / global asymptotic stability.

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熊友兵 , 李红智. 具有时滞及B-D功能反应的食物链系统周期解的存在性与全局渐近稳定性. 系统科学与数学, 2008, 28(3): 288-301. https://doi.org/10.12341/jssms10069
XIONG Youbing , LI Hongzhi. Existence and Global Asymptotic Stability of Periodic Solution in a Food-Chain System with Delays and Beddington-Deangelis Functional Response. Journal of Systems Science and Mathematical Sciences, 2008, 28(3): 288-301 https://doi.org/10.12341/jssms10069
中图分类号: 34K13    92D25   
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