| 一类关于Leslie-Gower捕食-被捕食时滞模型的局部Hopf分岔分析 |
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| 引用本文： | 张文,刘海鸿,张健.一类关于Leslie-Gower捕食-被捕食时滞模型的局部Hopf分岔分析[J].云南师范大学学报(自然科学版),2012,32(1):42-47. |
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| 作者姓名： | 张文 刘海鸿 张健 |
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| 作者单位： | 云南师范大学数学学院,云南昆明,650092 |
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| 基金项目： | 天元基金资助项目(10926167) |
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| 摘 要： | 主要研究时滞Leslie-Gower捕食-被捕食微分模型,将时滞τ作为分岔参量,讨论了正平衡点及分岔的存在性。进一步,应用规范理论与中心流形定理,判断了分岔的方向与周期解的稳定性。并给出了实例与数值模拟。
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| 关 键 词： | Leslie-Gower 时滞 中心流形 Hopf分岔 |
Bifurcations for a Delayed Leslie-Gower Predator-prey System |
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| ZHANG Wen
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LIU Hai-hong
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ZHANG Jian.Bifurcations for a Delayed Leslie-Gower Predator-prey System[J].Journal of Yunnan Normal University (Natural Sciences Edition),2012,32(1):42-47. |
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| Authors: | ZHANG Wen LIU Hai-hong ZHANG Jian |
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| Institution: | (Department of Mathematics,Yunnan Normal University,Kunming 650092,China) |
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| Abstract: | This paper is concerned with a two species Leslie-Gower predator-prey system with time delay.By regarding the delay τ as the bifurcation parameter,the stability of positive equilibrium and Hopf bifurcations are investigated.Furthermore,the direction of Hopf bifurcations and the stability of bifurcating periodic solutions are determined by applying the norm form theory and the center manifold theorem for functional differential equations.Finally,some numerical simulations are carried out for illustrating the theoretical results at the end of this paper. |
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| Keywords: | Leslie-Gower Delay Center manifold Hopf bifurcation |
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