具有抑制作用和离散时滞的捕食系统的Hopf分岔分析  

Analysis of Hopf Bifurcation in a Predator-Prey System of Population Allelopathy with a Discrete Delay

作　　者：王新慧[1] 刘海鸿[1] 

机构地区：[1]云南师范大学数学学院

出　　处：《云南民族大学学报（自然科学版）》2012年第4期286-291,共6页Journal of Yunnan Minzu University:Natural Sciences Edition

基　　金：云南省自然科学基金(2011FZ086)

摘　　要：研究了一类具有抑制作用和离散时滞的捕食-食饵模型,通过分析该模型在正平衡点的线性化方程及其相应的特征方程,研究了正平衡点渐近稳定性并证明了Hopf分岔的存在.通过应用规范型理论和中心流形定理,得到了确定Hopf分岔方向和分岔周期解的稳定性计算公式.最后,利用数值模拟验证了研究结果.A Lotka - Voherra two - species predator - prey system of population allelopathy with a discrete delay is studied. By linearizing the system at the positive equilibrium and analyzing the associated characteristic equation, the asymptotic stability of the positive equilibrium is investigated and Hopf bifurcations are demonstrated. Further- more, the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are determined by the normal form theory and the center manifold theorem for functional differential equations. Finally, some numerical simulations are carried out for illustrating the theoretical results.

关 键 词：Lotka—Volterra捕食-食饵系统 离散时滞 稳定性 HOPF分岔 周期解 抑制作用 

分 类 号：O175.13[理学—数学] O193[理学—基础数学]