一类食饵-捕食扩散模型分析  

Analysis of a prey-predator model with migration

作　　者：孙军芳[1] 张睿[1] 刘晶[1] 陈梅艳[1] 

机构地区：[1]兰州交通大学数理与软件工程学院,兰州730070

出　　处：《齐齐哈尔大学学报（自然科学版）》2007年第5期82-85,共4页Journal of Qiqihar University(Natural Science Edition)

摘　　要：在两种群相互作用的Lotka-Volterra模型的基础上考虑了一类食饵种群分布在2个斑块:一个斑块上食饵和捕食者相互作用且对捕食者种群进行捕获;而另一个斑块属于食饵保护区,没有捕食者进入且不允许对食饵种群进行捕获,并且食饵种群可以在2个斑块间进行扩散的食饵-捕食模型。讨论了平衡点的存在性,利用Hurwitz判别法证明了平衡点的局部渐近稳定性和通过构造李雅普诺夫函数,得到了平衡点全局渐近稳定的结论。In this paper, we consider a prey-predator system based on Lotka-Volterra model with prey dispersal in a two-patch environment, one is assumed to be a free harvesting zone where harvesting activity to predator species is existent, and prey and predator can interactive, and the other is a reserved zone where harvesting to prey is prohibited and no predator. Also, prey can migrate between the two-patch. The existence of equilibrium of the system is discussed. The local stability of equilibrium has been carried out using Hurwitz criteria. The global asymptotically stability of equilibrium is given by structuring Lyapunov function.

关 键 词：食饵-捕食 平衡点 全局稳定 

分 类 号：O175.1[理学—数学]