| 一类捕食与被捕食LV模型的扩散性质 |
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| 引用本文： | 张兴安.一类捕食与被捕食LV模型的扩散性质[J].系统科学与数学,1999,19(4):407-414. |
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| 作者姓名： | 张兴安 |
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| 作者单位： | 华中师范大学数学系!武汉４３００７９(张兴安，梁肇军)，中国科学院数学研究所!北京１０００８０(张兴安，陈兰荪) |
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| 基金项目： | 国家自然科学基金，湖北省自然科学基金 |
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| 摘 要： | 本文证明了一类带有扩散的捕食与被捕食Ｌｏｔｋａ－Ｖｏｌｔｅｒｒａ模型的如下性质：当该模型存在正平衡点时，它的一切正解是强持续生存的；当扩散率较小时，该系统的正平衡点是稳定的；当扩散率增大且位于某一开区间内变化时，该系统的正平衡点是不稳定的，而且分支出唯一的小振幅空间周期解；当扩散率继续增大时，该系统的正平衡点又变为稳定的．
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| 关 键 词： | 强持续生存 扩散率 斑块（patch） |
THE DISPERSAL PROPERTIES OF A CLASS OF PREDATOR-PREY LV MODEL |
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| Xing An ZHANG,Zhao Jun LIANG,Lan Sun CHEN.THE DISPERSAL PROPERTIES OF A CLASS OF PREDATOR-PREY LV MODEL[J].Journal of Systems Science and Mathematical Sciences,1999,19(4):407-414. |
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| Authors: | Xing An ZHANG Zhao Jun LIANG Lan Sun CHEN |
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| Institution: | (1)Dept.of Math.,Central China Normal Univ.,Wuhan 430079,P.R.China,Inst.of Math.,Academia Sci.,Beijing 100080,P.R.China;(2)Dept.of Math.,Central China Normal Univ.,Wuhan 430079,P.R.China;(3)Inst. of Math.,Academia Sci.,Beijing 100080,P.R.China |
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| Abstract: | This paper proves the following properties of a class of predator-prey Lotkavolterra model with diffusion. The positive solutions are of strong persistence if the model hasa positive equilibrium. The positive equilibrium is stable if the dispersal rate is small. Thepositive equilibrium is unstable and the system bifurcates a spatial periodic solution of smallamplitude if the dispersal rate is located in an interval. The positive equilibrium is stable if thedispersal rate is larger than the maximum of the interval. |
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| Keywords: | Strong persistence dispersal rate patch |
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