具有三时滞Lotka-Volterra互惠系统的Hopf分支(英文)  

Hopf Bifurcation for Lotka-Volterra Mutualist Systems with Three Delays

作　　者：张凤琴[1] 张雅婧[1] 

机构地区：[1]运城学院,山西运城044000

出　　处：《生物数学学报》2011年第2期223-233,共11页Journal of Biomathematics

基　　金：supported by the National Sciences Foundation of China(1 1071283);the Sciences Foundation of Shanxi(2009011005-3);the Major Subject Foundation of Shanxi

摘　　要：建立了具有三个时滞的Lotka-Volterra互惠系统;获得了正平衡点和Hopf分支存在的条件等;并对所获得的结果进行了数值模拟.A Lotka-Volterra cooperative model with three delays is introduced. By analyzing the distribution of the roots of the characteristic equation, we get the conditions of the positive equilibrium and the existence of Hopf bifurcations. Further, the explicit formulas which point out the stability and the direction of periodic solutions bifurcating from Hopf bifurcations are obtained by using the the normal theory and center manifold argument. Finally, numerical simulations are given to illustrate the mathematical results.

关 键 词：互惠系统 时滞 HOPF分支 稳定性 

分 类 号：O175.1[理学—数学]