| 比率型捕食者-食饵模型的稳定性与分支 |
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| 引用本文： | 肖氏武.比率型捕食者-食饵模型的稳定性与分支[J].襄樊学院学报,2007,28(8):9-12. |
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| 作者姓名： | 肖氏武 |
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| 作者单位： | 襄樊学院,数学系,湖北,襄樊,441053 |
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| 摘 要： | 对比率依赖型捕食者-食饵模型进行研究.关于捕食者的死亡率,不仅考虑捕食者的自然死亡因素,还应加入种内之间争夺资源及其它原因引起的死亡因素,即捕食者之间密度制约因素,得到了系统稳定性的条件;并通过分支理论得到了极限环的存在性.通过研究退化的唯一正平衡点,得到了Bogdanov-Takens分支,分支出同宿圈.
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| 关 键 词： | 比率依赖 极限环 Hopf分支 Bogdanov-Takens分支 |
| 文章编号： | 1009-2854(2007)08-0009-04 |
| 修稿时间： | 2007年5月24日 |
Stability and Bifurcation of a Ratio-Dependent Predator-Prey System |
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| XIAO Shi-wu.Stability and Bifurcation of a Ratio-Dependent Predator-Prey System[J].Journal of Xiangfan University,2007,28(8):9-12. |
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| Authors: | XIAO Shi-wu |
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| Institution: | XIAO Shi-wu |
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| Abstract: | A ratio-dependent predator-prey system is studied.The death rate of predator is composed by the natural mortality rate and the other death rate caused by the intraspecies competition or other factors,i.e.the predator density dependent.Conditions for the stability of system are obtained.The limit cycle is obtained by the bifurcation theory.The Bogdanov-Takens bifurcation is studied when there is a unique degenerate positive equilibrium. |
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| Keywords: | Ratio-dependence Limit cycle Hopf bifurcation Bogdanov-Takens bifurcation |
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