一类具有阶段结构和时滞的捕食模型的稳定性及Hopf分支(英文)

Stability and Hopf Bifurcation in a Predator-prey Model with Stage Structure and Time Delay

研究一类具有阶段结构和时滞的捕食模型.通过特征方程分别分析了正平衡点和边界平衡点的局部稳定性,到了系统Hopf分支存在的充分条件.通过规范型理论和中心流型定理,给出了确定Hopf分支方向和分支周期解的稳定性的计算公式.

A predator-prey system with time delay due to the gestation of the predator and stage structure for both the predator and the prey is proposed and investigated.By analyzing the corresponding characteristic equations,the stability of a positive equilibrium and two boundary equilibria of the system is discussed,respectively.Further,the existence of Hopf bifurcations at the positive equilibrium is also studied.By using the normal form theory and center manifold theorem,formulae determining the direction of bifurcations and the stability of bifurcating periodic solutions are given.