时滞食饵-捕食系统平衡点的稳定性和周期解  

Stability and periodic solutions in a predator-prey system with delays

作　　者：李小玲[1] 胡广平[1] 

机构地区：[1]南京信息工程大学数理学院,南京210044

出　　处：《兰州大学学报（自然科学版）》2009年第2期81-84,共4页Journal of Lanzhou University(Natural Sciences)

基　　金：南京信息工程大学校内基金项目

摘　　要：考虑具有多个离散时滞的食饵-捕食系统,讨论了系统平衡点的稳定性.选取其中的一个时滞作为分支参数,运用Hopf分支定理得到了周期解的局部存在性.最后运用泛函微分方程的全局Hopf分支定理得到了周期解的大范围存在性.A predator-prey system with three delays was studied in this paper. The stability of the positive equilibrium was derived and, one of delays taken as the bifurcation parameter, the existence result of periodic solutions was obtained by using Hopf bifurcation theorem. In addition, the global existence results of periodic solutions were established by using a global Hopf bifurcation theorem of FDEs.

关 键 词：平衡点 线性化方程 HOPF分支 时滞 

分 类 号：O175.7[理学—数学]