| 具扩散的捕食与被捕食Lotka—Volterra模型研究 |
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| 引用本文： | 欧伯群,秦发金.具扩散的捕食与被捕食Lotka—Volterra模型研究[J].西北师范大学学报,2001,37(2):28-33. |
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| 作者姓名： | 欧伯群 秦发金 |
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| 作者单位： | [1]钦州高等师范专科学校数学系，广西钦州535000 [2]柳州高 |
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| 摘 要： | 证明了一类具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，它的一切正解是有界的，并且是强持续生存的；当扩散率较小时，系统的正平衡点是稳定的；当扩散率增大且在某一开区间变化时，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，系统的正平衡点又变成稳定的。
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| 关 键 词： | Lotka－Volterra模型 扩散率 稳定 正平衡点 强持续生存 小振幅空间周期解 捕食 |
| 文章编号： | 1001-988Ⅹ(2001)02- 0028-06 |
| 修稿时间： | 2000年4月5日 |
Study on a Lotka-Volterra model of diffuse predator-prey |
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| OU Bo qun ,QIN Fa jin.Study on a Lotka-Volterra model of diffuse predator-prey[J].Journal of Northwest Normal University Natural Science (Bimonthly),2001,37(2):28-33. |
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| Authors: | OU Bo qun QIN Fa jin |
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| Institution: | OU Bo qun 1,QIN Fa jin 2 |
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| Abstract: | A class of Lotka Volterra model of diffuse predator prey is analysed,which has the following features:if there is a positive balance point in this system,all its positive balance points are bounded and strongly persistence;if the model has a small diffuse rate,its positive balance point will fluctuate steadily,but when the diffuse rate increases to a certain degree and keeps changing in a certain open interval,the positive balance point will fluctuate unsteadily and branch out one periodic solution within a small amplitude;if the diffuse rate keeps increasing and goes beyond the certain degree,the positive balance point will fluctuate in a steady rate again. |
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| Keywords: | Lotka-Volterra model diffuse rate steady balance point strongly perrsistence |
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