带Holling Ⅲ型功能反应函数的捕食-食饵生态经济模型的Hopf分支

Hopf bifurcation for a predator-prey biological economic system with Holling type Ⅲ functional response

分析了一类考虑带HollingⅢ型功能反应函数和食饵收获的捕食-食饵生态经济系统.运用微分代数系统理论和Hopf分支理论研究了一类系统的Hopf分支.考虑了一个由于经济因素得到的微分代数方程而不是以前所研究的普通捕食-食饵模型的动力学行为.其中经济利润是作为一个正的分支参数给出的.当经济利润增大到某一个阈值时,会出现Hopf分支.

In this paper,we analyze a biological economic system which considers a prey-predator system with Holling type Ⅲ functional response and harvest effort on prey.Hopf bifurcation of the proposed system is investigated by using the differential-algebraic system theory and Hopf bifurcation theory.Our model is described by differential-algebraic equations due to the economic factor other than previous researches on the dynamic behaviors of predator-prey systems.Here the economic profit is given as a positive bifurcation parameter.It is found that Hopf bifurcation will occur as the economic profit increases beyond a certain threshold.