| 食饵有常数放养率的广义Rosenzweig-Macarthur系统 |
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| 引用本文： | 杨德全,刘影.食饵有常数放养率的广义Rosenzweig-Macarthur系统[J].大学数学,2000(3). |
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| 作者姓名： | 杨德全 刘影 |
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| 作者单位： | 四平师范学院数学系!四平136000 |
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| 基金项目： | 吉林省教委自然科学基金，四平师范学院自然科学基金 |
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| 摘 要： | 本文运用 Liapunov第二方法 ,研究了食饵有常数放养率的广义 Rosenzweig-Macarthur系统x=f ( x) -yφ( x) +H ,y=h( y) -e+Kφ( x) ]唯一正平衡点的稳定性 .并利用 Poincare-Bendixon环域定理及张芷芬唯一性定理 ,论证了在 R+ 2 ={( x,y)∶x>0 ,y>0 }内极限环的存在唯一性及其稳定性 .
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| 关 键 词： | Liapunov函数 稳定性 Poincare-Bendixon环域 极限环 |
On the Generalized Rosenzweig-MacArthur System of Buitedfoods Having the Constant Breeding Rate |
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| YANG De quan,LIU Ying.On the Generalized Rosenzweig-MacArthur System of Buitedfoods Having the Constant Breeding Rate[J].College Mathematics,2000(3). |
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| Authors: | YANG De quan LIU Ying |
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| Abstract: | By utilizing Liapunov's second methods, we discussed steadiness of unique positive balanced points in the generalized Roseuzweig MacArthur system as follow =f(x)-yφ(x)+H, =h(y)-e+φ(x)]. that buited foods having the constant breeding rate. We also proved the existed unique quality and steadiness of the limited ring in R + 2={(x,y)∶x>0,y>0} . For this purpose, we made use of poincare Bendixin ring field and zhang zhifen unique theorems. |
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| Keywords: | Liapunov function steadiness poincare Bendixon ring field limited ring |
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