一类稀疏效应下捕食┐被捕食者系统极限环的存在性和唯一性

Existence and Uniqueness of Limit Cycle about Predator Prey System with Sparssing Effect

本文研究捕食者种群具有线性密度制约的一类稀疏效应下捕食－被捕食者系统ｘ＝ｘ（ａｘ－ｃｘ３－ｂｙ），ｙ＝ｙ（－α＋βｘ－γｙ）．（＊）得到：（１）当Ａ１＜Ａ１，Ａ２＜Ａ２，Ａ３＞Ａ３时，系统（＊）在第一象限内存在极限环；（２）当Ａ２＜Ａ２，Ａ３＞Ａ３时。

A predator prey model with sparrssing effect is considered as follows:=x(ax-cx 3-by);=y(-α+βx-γy)(*). The main result is as follows: (1) when A 1< 1,A 2< 2,A 3> 3,there at leastn exists a limit cycle of the system(*); (2) when A 2< 2,A 3> 3,there exists unique limit cycle of the system(*).