| 双时滞比率依赖Holling-Ⅳ和Leslie型捕食-食饵系统的Hopf分支 |
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| 引用本文： | 郑宗剑.双时滞比率依赖Holling-Ⅳ和Leslie型捕食-食饵系统的Hopf分支[J].北华大学学报(自然科学版),2015(1):9-16. |
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| 作者姓名： | 郑宗剑 |
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| 作者单位： | 四川文理学院数学与财经学院,四川 达州,635000 |
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| 基金项目： | 四川省教育厅自然科学基金项目，四川革命老区发展研究中心项目，四川文理学院校级重点课题 |
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| 摘 要： | 研究了一类双时滞基于比率依赖简化Holling-Ⅳ型功能性反应且具有Leslie形式的捕食者数量反应的捕食-食饵系统,通过分析系统对应的特征方程,得到各种情形下的正平衡点局部稳定及Hopf分支存在的充分条件,并通过数值模拟验证了结果的正确性.
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| 关 键 词： | Hopf分支 捕食-食饵系统 时滞 平衡点 Holling-Ⅳ |
Hopf Bifurcation of Ratio-dependent Holling IV and Leslie Type Predator-prey System with Two Delays |
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| Zheng Zongjian.Hopf Bifurcation of Ratio-dependent Holling IV and Leslie Type Predator-prey System with Two Delays[J].Journal of Beihua University(Natural Science),2015(1):9-16. |
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| Authors: | Zheng Zongjian |
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| Institution: | Zheng Zongjian;College of Mathematics and Finance-Economics,Sichuan University of Arts and Sciences; |
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| Abstract: | A predator-prey system of ratio-dependent simplified Holling-Ⅳfunctional response and the predator’ s numerical response of Leslie form with two delays is considered. By analyzing the associated characteristic equation,the local stability of the equilibrium is obtained. Hopf bifurcation ’ s existence is discussed. Finally, numerical simulation is done for instance to verify the main conclusion. |
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| Keywords: | Hopf bifurcation predator-prey system delay equilibrium Holling-Ⅳ |
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