THE PREDATOR-PREY MODEL WITH TWO LIMIT CYCLES  

作　　者：任永泰 韩莉 

机构地区：[1]Earth East Normal University [2]Liaoning Normal Universityhis paper investigates the predator-prey system:x=k_1(x-ax)-k(x)y,y=(-k_3+βk(x)ywit.k(x)=k_2x, x≤x, k_2x, x>τ,where α, β, τ [3]k_1, k_2, k_3 are positive constants.The main results are as follows(i) In case k_3-βk_2τ≥0 system (1) has no limit cycle.(ii) In case k_3-βk_2τ<0, k_1+k_3-βk_2τ> and for O<α<<1, system (1) at least has two limitcycles.

出　　处：《Acta Mathematicae Applicatae Sinica》1989年第1期30-32,共3页应用数学学报（英文版）

摘　　要：This paper investigates the predator-prey system:x=k_1(x-ax)-k(x)y,y=(-k_3+βk(x)ywit.k(x)=k_2x, x≤x, k_2x, x>τ,where α, β, τ; k_1, k_2, k_3 are positive constants.The main results are as follows(i) In case k_3-βk_2τ≥0 system (1) has no limit cycle.(ii) In case k_3-βk_2τ<0, k_1+k_3-βk_2τ> and for O<α<<1, system (1) at least has two limitcycles.This paper investigates the predator-prey system:x=k_1(x-ax)-k(x)y,y=(-k_3+βk(x)ywit.k(x)=k_2x, x≤x, k_2x, x>τ,where α, β, τ; k_1, k_2, k_3 are positive constants.The main results are as follows(i) In case k_3-βk_2τ≥0 system (1) has no limit cycle.(ii) In case k_3-βk_2τ<0, k_1+k_3-βk_2τ> and for O<α<<1, system (1) at least has two limitcycles.

关 键 词：TH LINE 

分 类 号：O1[理学—数学]