一类多时滞有捕获的Leslie-Gower型捕食系统的Hopf分支  

A Hopf Bifurcation in a Leslie-Gower Predator-prey System with Delays and Harvesting

作　　者：王玲[1] 赵中建[2] 张广[3] 

机构地区：[1]中北大学数学系,山西太原030051 [2]华北水利水电学院,河南郑州450011 [3]天津商业大学理学院,天津300134

出　　处：《华北水利水电学院学报》2010年第2期104-106,共3页North China Institute of Water Conservancy and Hydroelectric Power

摘　　要：通过选取时滞为分支参数,分析了时滞对一类捕食-被捕食动力系统的影响.应用规范型和中心流形理论,得到了分支方向和周期解的稳定性计算公式.证明了该系统在正平衡点产生Hopf分支的充分条件,并为生物资源的实际开发与管理提供了必要的理论依据.By choosing the delay as a bifurcation parameter,the influence of time delays on the predator-prey dynamic system was analyzed.Based on the normal form theory and center manifold reduction,explicit formula determining the properties of bifurcating periodic solutions were derived.The sufficient conditions were proved in existence that the system produced Hopf bifurcation at the positive equilibrium points,and the necessany theoretical basis was provided for development and management of biological resources.

关 键 词：捕食-被捕食 时滞 捕获 HOPF分支 

分 类 号：O29[理学—应用数学] O33[理学—数学]