| 具有收获和Beddington-DeAngelis功能反应的捕食-食饵模型 |
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| 引用本文： | 章培军1,2,王震1,2,杨颖惠3. 具有收获和Beddington-DeAngelis功能反应的捕食-食饵模型[J]. 华侨大学学报(自然科学版), 2017, 0(4): 579-584. DOI: 10.11830/ISSN.1000-5013.201704025 |
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| 作者姓名： | 章培军1 2 王震1 2 杨颖惠3 |
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| 作者单位： | 1. 西京学院 理学院, 陕西 西安 710123;2. 西京学院 智能控制技术研发中心, 陕西 西安 710123;3. 西南交通大学 数学学院, 四川 成都 611756 |
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| 摘 要： | 研究食饵具有阶段结构,捕食者具有收获和时滞的Beddington-DeAngelis功能反应的捕食-食饵模型.选取合适的收获率,通过分析相应平衡点处的特征方程,得到各平衡点局部渐近稳定的条件.以时滞τ为分支参数,运用Hopf分支理论,得到当τ经过临界值τ0时系统出现Hopf分支.最后,用Matlab软件进行数值仿真,并验证结论的正确性.
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| 关 键 词： | Beddington-DeAngelis功能反应 捕食-食饵模型 时滞 阶段结构 Hopf分支 |
Predator-Prey Model With Beddington-DeAngelis Functional Response and Harvesting |
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| ZHANG Peijun1,' target="_blank" rel="external">2,WANG Zhen1,' target="_blank" rel="external">2,YANG Yinghui3. Predator-Prey Model With Beddington-DeAngelis Functional Response and Harvesting[J]. Journal of Huaqiao University(Natural Science), 2017, 0(4): 579-584. DOI: 10.11830/ISSN.1000-5013.201704025 |
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| Authors: | ZHANG Peijun1,' target=" _blank" rel=" external" >2,WANG Zhen1,' target=" _blank" rel=" external" >2,YANG Yinghui3 |
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| Affiliation: | 1. School of Science, Xijing University, Xi’an 710123, China; 2.Intelligent Control Technology Research and Development Center, Xijing University, Xi’an 710123, China; 3. School of Mathematics, Southwest Jiaotong University, Chengdu 611756, China |
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| Abstract: | A predator-prey model with Beddington-DeAngelis functional response of predator with harvesting and time delay and the stage structure for prey are investigated in this paper. Select the appropriate harvest rate, the conditions for the local asymptotic stability of the equilibrium point are obtained by analyzing the characteristic equation of the corresponding equilibrium point; by means of the Hopf bifurcation theorem and considering the delay τ as a bifurcation parameter, Hopf bifurcation occurs when τ passes through the critical value τ0. Finally, Matlab is employed to carry out numerical simulation to verify our results. |
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| Keywords: | Beddington-deAngelis functional response predator-prey model time delay stage structure Hopf bifurcation |
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