关于一类捕食与被捕食种群关系数学模型研究

Study on Mathematical Model of a Class of Predator Communituy and Prey Community

本文通过对一个微分方程组的奇点分析，轨线分布情况及全局稳定性的讨论（文中对捕食者种群的吸收率K（x）用三段函数来表示），得出结论：无论两个种群的原始数量如何，随时间的推移，总要稳定在正平衡点（1／2，3r／8）上，从而揭示了错综复杂的生物圈内，捕食者种群与被捕食者种群间的捕食关系．

Through the singularity analysis on a Calculus system of equations, trajectory distribution circumstance and overall situation disscusion (This article uses three-stage function to represent absorptivity of predator community-k (x)), this article eventually concludes, despite of primitive quantity, that the two communities always keep stability at the balance point (1 /2 ,, 3r/8 ) with the lapse of time. Thus it reveals the relationship between predator community and prey community with in a complicated biosphere.