一类具有阶段结构的时滞捕食系统的周期解

Periodic Solution of a Delayed Predator-prey System with Stage Structure

研究一类捕食者具有阶段结构和Crowley-Martin功能性反应的时滞捕食系统.通过分析特征方程根的分布,得到系统正平衡点的局部稳定性和局部Hopf分叉的存在性的充分条件.进一步,利用中心流形定理和规范型理论,给出确定Hopf分叉方向和分叉周期解稳定性的计算公式.最后,利用仿真实例证明了理论分析结果的正确性.

In this paper,we analyze a delayed and stage- structured predator- prey system with Crowley-Martin functional response. By analyzing the distribution of the roots of the associated characteristic equation,sufficient conditions for the local asymptotic stability of the positive equilibrium and the existence of the local Hopf bifurcation are obtained. Further,explicit formulae for determining the direction of the Hopf bifurcation and the stability of the periodic solutions are derived by using the normal form theory and center manifold argument. Finally, some numerical simulations are presented to support the theoretical results.