一类稀疏效应下功能性反应系统的拓扑结构分析

Topological structure analysis of a class of functional response predator-prey system with scanty effect

分析了一类稀疏效应下第Ⅱ类功能反应捕食系统的拓扑结构随捕食种群死亡率c的变化规律,提供系统关于生态稳定方面的一些有用信息.得出结论:当0<c<c1时,两种群必将同时灭绝;当c1<c<c3时,两种群有保持生态平衡的可能;当c3<c<+∞时,捕食种群必将灭绝,而食饵种群的数量必将稳定在k.

A change law of the topological structure of a class of functional response predator-prey system with scanty effect is discussed, when the death rate c of the predator of this system is changing monotonously. Then the useful information of the ecological balance of this system is provided. The conclusion is as follows： When 0〈 c〈 c1 ,then these two species must be extinct together; When c1〈 c 〈c3, then these two species may keep the ecological balance; When c3 〈 c 〈 ＋∞, then the predator species must be extinct, and the prey species must be stable at the number k.