一类带无选择性捕获和时滞的捕食食饵系统的Hopf分支分析

摘要

本文主要研究了一个改进的带时滞和无选择捕获函数的捕食-食饵生态经济系统的稳定性和Hopf分支.利用微分代数系统的稳定性理论和分支理论,得到了系统正平衡点稳定性的条件,以及当时滞τ作为分支参数时系统产生Hopf分支的条件.对Leslie-Gower捕食-食饵模型进行了一定程度的完善,使得建立的模型更符合实际情况,因此得到的结论也更加科学.%In this paper, we mainly study the Hopf bifurcation and the stability of modified predator-prey biological economic system with nonselective harvesting and time delay. By using the stability and bifurcation theory of differential-algebraic system, the conditions for stability of the positive equilibrium point are obtained, let time delay as bifurcation parameter, the existence of Hopf bifurcation and direction of Hopf bifurcation are obtained. We have improved the Leslie-Gower predator-prey system, make the system which we established more practical, so the conclusions are made more scientific.