一个带有离散和分布时滞的Holling-Ⅳ型捕食被捕食模型的稳定性和分支

Stability and Hopf Bifurcation of a Holling Type Ⅳ Predator-Prey System with Diecrete and Distribute Delays

本文研究了一个带有离散和分布时滞的Holling-IV型功能反应的捕食与被捕食模型,将离散时滞r看作分支参数,讨论了正平衡点的局部稳定性和Hopf分支,利用Routh-Hurwitz定理得到了平衡点局部渐近稳定的充分条件.通过分析相应的特征方程,发现随着r穿越某临界值,Hopf分支会发生,并且可能出现小范围周期解.

A Holling type IV predator-prey model with diecrete and distribute delays is investigated,where the discrete delay π is regarded as a parameter.Its dynamics are studied in terms of local stability analysis and Hopf bifurcation analysis.Using the Routh-Hurwitz criterion,the sufficient conditions of locally asymptotic stability of the positive equilibrium point is derived.By analyzing the associated characteristic equation,it is found that Hopf bifurcation occurs when t crosses some critical value.Then,small amplitude periodic solutions arise.