一类具有时滞和收获的捕食模型的稳定性和Hopf分支  

Stability and Hopf Bifurcation of a Predator-prey Model with Time Delay and Harvesting

作　　者：王志丽[1] 徐瑞[1] 

机构地区：[1]军械工程学院数学系,河北石家庄050003

出　　处：《北华大学学报（自然科学版）》2014年第1期1-6,共6页Journal of Beihua University（Natural Science）

摘　　要：研究一类含有常数收获率和时滞的捕食-被捕食模型,通过分析特征方程研究了正平衡点的稳点性及Hopf分支的存在性,应用中心流形定理和规范型理论,得到了确定Hopf分支方向和分支周期解稳定性的计算公式,最后对所得结果进行了数值模拟.A predator-prey model with time delay and harvesting is considered. The local stability of positive equilibrium is established by analyzing the corresponding characteristic equation. The direction of bifurcations and the stability of bifurcating periodic solutions are derived by using the normal form theory and the center manifold theorem. Finally,numerical simulations are carried out to illustrate the theoretical results.

关 键 词：时滞 收获率 稳定性 HOPF分支 周期解 

分 类 号：O175.14[理学—数学]