摘要
本文研究带Holling-II型功能反应的具有退化承载能力的捕食者–食饵模型的稳定性与Hopf分支。首先讨论平衡点的局部渐近稳定性,然后以退化系数ρ为分支参数,给出Hopf分支存在的条件。最后利用规范型理论和中心流形定理分析Hopf分支的方向及分支周期解的稳定性。
In this paper, we study the stability and the Hopf bifurcation of apredator-prey model with degenerate carrying capacity with Holling-II type of functional response. Firstly, the local asymptotic stability of the equilibrium point is discussed. Then, the existence condition of the Hopf bifurcation is given by taking the degradation coefficient ρ as the branching parameter. Finally, the direction of the Hopf bifurcation and the stability of its periodic solution are analyzed by means of canonical theory and central manifold theorem.
出处
《理论数学》
2022年第1期62-70,共9页
Pure Mathematics
