具常数投放率的食饵—捕食者系统定性分析

Qualitative Analysis of Predator-Prey System with Constant Rate Stoking

对一类广义具常数投放率的食饵—捕食者两类种群模型的定性分析,讨论了系统平衡点的稳定性,用Poincare-Bendixson环域定理得到平衡点外存在稳定极限环的条件。同时对相应结论的生态学意义给予说明,通过用计算机软件Maple进行图形绘制,能够清晰了解轨线的走向和趋势,从而证明了理论分析的正确性。

In this paper, we studied a predator-prey system with constant rate stoking. We disscussed the stability of equilibrium, used the Poincare-Bendixson＇s annular theorem to get some sufficient conditions for the existence and stability for limit cycles of such systems stable of the limit cycle around the positive equilibrium of the system, at the same time given meaning to the corresponding conclusions on the ecology. Through carrying on sketch to design with the computer software Maple, we can clearly understand line direction and trends, in order to demonstrate the validity of qualitative for differential power system was proved.