带有多时滞和Holling第Ⅲ类功能性反应的生态经济微分代数系统的稳定性与Hopf分支

摘要

A differential-algebraic biological economic system with time delay and Holling type Ⅲ functional response is considered,into which are incorporated a constant prey refuge and prey harvesting.A sufficient condition for the existence of a positive equilibrium is discussed and then an ordinary differential equation is transformed from the system by homeomorphic transformation.The time delay is considered as a bifurcation parameter,and the stability and Hopf bifurcation of the system were analyzed based on the characteristic root method and the bifurcation theorem.It is found that the Hopfbifurcation will occur when the bifurcation parameter is via an exceptive value.Numerical simulations illustrate the effectiveness of our results.%建立并分析了一个具有多时滞和Holling第Ⅲ类功能性反应的生态经济微分代数系统.得到了正平衡点及正平衡点存在的条件,利用同胚变换将微分代数系统转化为常微分方程,对该方程进行线性化,得到含有多时滞的非线性特征方程.通过讨论得到平衡点局部渐近稳定的充分条件,当时滞参数通过某些特定值时,系统在平衡点附近出现Hopf分支现象.数值模拟验证了理论分析结果.