| 一类具有时滞的比率依赖捕食者-食饵模型的全局Hopf分支 |
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| 引用本文： | 赵汇涛. 一类具有时滞的比率依赖捕食者-食饵模型的全局Hopf分支[J]. 数学杂志, 2016, 36(1): 191-198 |
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| 作者姓名： | 赵汇涛 |
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| 作者单位： | 周口师范学院数学与信息科学系, 河南 周口 466001 |
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| 基金项目： | 河南省教育厅资助项目(13A110108);河南省科技厅资助项目(122300410417). |
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| 摘 要： | 本文研究了一类比率依赖的捕食者-食饵模型的Hopf分支问题,运用吴建宏等人利用等变拓扑度理论建立起的一般泛函微分方程的全局分支理论,得到了由系统的正平衡点分支出来的周期解的全局存在性,最后利用数值模拟验证了理论分析的正确性.
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| 关 键 词： | 比率依赖 捕食者-食饵模型 稳定性 全局Hopf分支 |
| 收稿时间： | 2013-09-05 |
| 修稿时间： | 2014-04-21 |
GLOBAL HOPF BIFURCATION OF A RATIO-DEPENDENT PREDATOR-PREY MODEL WITH TIME DELAY |
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| ZHAO Hui-tao. GLOBAL HOPF BIFURCATION OF A RATIO-DEPENDENT PREDATOR-PREY MODEL WITH TIME DELAY[J]. Journal of Mathematics, 2016, 36(1): 191-198 |
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| Authors: | ZHAO Hui-tao |
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| Affiliation: | Department of Math. and Information Science, Zhoukou Normal University, Zhoukou 466001, China |
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| Abstract: | This paper is concerned with a ratio-dependent predator-prey model with time delay. By using a global Hopf bifurcation result of general functional differential equations due to Wu Jianhong etc., the global existence results of periodic solutions bifurcating from Hopf bifurcations are established. Finally, numerical simulations are also included to support the theoretic analysis. |
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| Keywords: | ratio-dependent predator-prey model stability global Hopf bifurcation |
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