具有时滞和阶段结构的捕食系统的分支分析

Bifurcation Analysis of Predator-prey System with Time Delay and Stage Structure

研究了一类食饵具有阶段结构的时滞捕食系统,通过分析特征方程,以捕食者的消极负反馈时滞为参数,讨论了系统正平衡点的局部稳定性和Hopf分支的存在性,利用中心流形定理和规范型理论,给出了确定Hopf分支方向和分支周期解稳定性的计算公式.

A delayed predator-prey system with stage structure for the prey is concerned. The stability and the existence of Hopf bifurcation at the coexistence equilibrium is discussed by analyzing the associated characteristic equation. An explicit formula for determining the stability and the direction of periodic solutions that bifurcates from Hopf bifurcation is derived by using the normal form theory and center manifold argument.