食饵具庇护所的基于比率捕食-食饵模型的全局稳定性和分支

陈柳娟, 陈凤德

数学学报 ›› 2014, Vol. 57 ›› Issue (2) : 301-310.

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中国科学院数学与系统科学研究院期刊网
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数学学报 ›› 2014, Vol. 57 ›› Issue (2) : 301-310. DOI: 10.12386/A2014sxxb0030
论文

食饵具庇护所的基于比率捕食-食饵模型的全局稳定性和分支

    陈柳娟1, 陈凤德2
作者信息 +

Global Stability and Bifurcation of a Ratio-Dependent Predator-Prey Model with Prey Refuge

    Liu Juan CHEN1, Feng De CHEN2
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文章历史 +

摘要

研究一类食饵具庇护所的基于比率捕食-食饵模型，得到该模型的全局稳定、极限环以及Hopf分支等的一系列充分条件.研究表明当模型捕食种群转化率、死亡率和半饱和常数满足一定条件时，食饵庇护量不影响捕食、食饵两种群的共存. 一旦该条件不满足，则食饵庇护量具有稳定化作用. 数值模拟验证了所得结论的可行性.

Abstract

A ratio-dependent predator-prey model incorporating a prey refuge is investigated and a series of sufficient conditions on global stability, limit cycle and Hopf bifurcation are obtained. The results show that when the transformation rate, mortality and the half-saturation constant of predator population satisfy certain conditions,prey refuge has no influence on the coexistence of predator and prey species. Once the condition is not satisfied, then prey refuge has stabilization effect. Numerical simulations are performed to illustrate the feasibility of our results.

关键词

食饵庇护所 / Hopf 分支 / transcritical 分支 / 全局稳定 / 极限环

Key words

prey refuge / Hopf bifurcation / transcritical bifurcation / global stability / limit cycle

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陈柳娟, 陈凤德. 食饵具庇护所的基于比率捕食-食饵模型的全局稳定性和分支. 数学学报, 2014, 57(2): 301-310 https://doi.org/10.12386/A2014sxxb0030
Liu Juan CHEN, Feng De CHEN. Global Stability and Bifurcation of a Ratio-Dependent Predator-Prey Model with Prey Refuge. Acta Mathematica Sinica, Chinese Series, 2014, 57(2): 301-310 https://doi.org/10.12386/A2014sxxb0030

参考文献

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基金

福建省自然科学基金（2011J01007）；福建省科技创新平台计划资助项目（2009J1007）
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