| 一类捕食-食饵模型的共存性 |
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| 引用本文： | 刘娜,聂华.一类捕食-食饵模型的共存性[J].陕西师范大学学报,2012(3):12-15. |
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| 作者姓名： | 刘娜 聂华 |
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| 作者单位： | 陕西师范大学数学与信息科学学院 |
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| 基金项目： | 国家自然科学基金资助项目(11126201,11001160);陕西省自然科学基础研究计划项目(2009JQ1007) |
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| 摘 要： | 研究了一类具有一般形式反应函数的捕食-食饵模型的正解.给出了正解的先验估计,利用不动点指标原理讨论了正解的存在性.通过计算degW′(I-F,D)、indexW′(F,(0,0))和indexW′(F,(θ,0)),得出食饵和捕食者可以共存当且仅当捕食者的死亡率c控制在下限-d2λ0和上限-λ1(d2,-efv(θ,0))之间,且食饵的固有增长率超过d1λ0.
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| 关 键 词： | 捕食-食饵 正解 不动点指标原理 |
Coexistence in a predator-prey model |
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| LIU Na,NIE Hua.Coexistence in a predator-prey model[J].Journal of Shaanxi Normal University: Nat Sci Ed,2012(3):12-15. |
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| Authors: | LIU Na NIE Hua |
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| Institution: | *(College of Mathematics and Information Science, Shaanxi Normal University,Xi′an 710062,Shaanxi,China) |
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| Abstract: | The positive solutions are investigated for a predator-prey model with general functional response.A priori estimation to the positive solutions of the model is given,and the fixed point index theory is utilized for discussing the existence of the positive solutions.By calculating degW′(I-F,D),indexW′(F,(0,0)) and indexW′(F,(θ,0)),we obtain that predator and prey coexist if and only if predator′s death rate c is controlled between the lower limit-d2λ0 and the upper limit-λ1(d2,-efv(θ,0)),and prey′s inherent growth rate is lager than d1λ0. |
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| Keywords: | predator-prey positive solution fixed point index principle |
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