多时滞三种群系统的Hopf分支  

HOPF BIFURCATION OF THREE SPECIES SYSTEM WITH TIME DELAYS

作　　者：王希[1,2] 张凤琴[2] 张雅婧[2] 

机构地区：[1]中北大学理学院,太原030051 [2]运城学院,运城044000

出　　处：《系统科学与数学》2010年第4期530-540,共11页Journal of Systems Science and Mathematical Sciences

基　　金：山西省自然科学基金项目(2009011005-3);山西省重点扶持学科项目;山西省科技开发项目(2007151)

摘　　要：讨论了具有两个时滞的3种群模型,分析了系统正平衡点的稳定性和Hopf分支的存在性;然后利用中心流形定理和规范型方法,给出了确定分支周期解的分支方向与稳定性的计算公式,利用数值模拟验证了所得结论.In this paper, a three species system with two time delays is studied. The stability of the positive equilibrium and the existence of Hopf bifurcation are investigated. By using the normal form theory and center manifold argument, the explicit formulae which determine the stability, the direction and the other properties of bifurcating periodic solutions are derived. Finally some numerical simulations are carried out to illustrate the obtained results.

关 键 词：种群时滞模型 HOPF分支 稳定性 中心流形定理 规范型 

分 类 号：O175[理学—数学]