一类具有Allee影响的捕食与被捕食模型  

The Dynamic of Predator-preymodel with Allee Effect in the Prey

作　　者：王静[1] 薛亚奎[1] 

机构地区：[1]中北大学数学系,山西太原030051

出　　处：《数学的实践与认识》2008年第10期136-140,共5页Mathematics in Practice and Theory

基　　金：国家自然科学基金(10471040);山西省青年基金(20041004);山西省教育厅科技研究开发(20061025)

摘　　要：分析并建立了具有Allee影响的捕食与被捕食模型,被捕食者由于自身繁殖或是被捕食而具有了Allee效应,分别讨论了强Allee和弱Allee对被捕食种群的影响,讨论了解的有界性和各平衡点的存在性,并证明了各平衡点的局部渐近稳定性,进一步通过构造适当的Lyapunov函数分析了正平衡点E*的全局渐近稳定性.We analyze and formulate the Predator-prey model with Allee effect in the prey. The Allee effect in prey may be caused by predation or processes inherent to the prey life history. We also discussed the different effects on prey with the strong Allee effect or the weak Allee effect. And we study boundness of solutions and the existence of the equilibria, obtain the sufficient conditions of locally asymptotically stable of the equilibria, criterion, furthermore, analyze the global stability of the equilibria by constructing appropriate Lyapunov functions.

关 键 词：Allee 捕食-被捕食模型 渐近稳定 全局稳定 

分 类 号：O175[理学—数学]