具有收获率和Holling-Ⅱ型功能反应函数的时滞系统的定性分析

Qualitative Analysis of Time-delay Systems with Harvest Rate and Holling-Ⅱ Functional Response Functions

考虑具有收获率的Holling-Ⅱ型功能反应函数的食饵-捕食模型,通过详细分析系统在正平衡点E处线性化系统的特征方程的根在复平面上的分布,讨论模型正平衡点E的稳定性分析.最后利用Matlab软件包对相应的理论结果进行了数值验证.

A predator-prey model with harvest rate and Holling-Ⅱ functional response function is considered.By detailed analysis of the distribution of the roots of the characteristic equation of the linearized system of the original system at the positive equilibrium point E*in the complex plane,an analysis is made of the stability of the positive equilibrium point E*in the model.Finally,the corresponding theoretical results are given a numerical verification by Matlab software package.