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THE PREDATOR-PREY MODEL WITH TWO LIMIT CYCLES
作者姓名:任永泰  韩莉
作者单位:Earth East Normal University,Liaoning Normal University
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>0, and for O<α<<1, system (1) at least has two limitcycles.


The predator-prey model with two limit cycles
Yongtai Ren,Li Han.THE PREDATOR-PREY MODEL WITH TWO LIMIT CYCLES[J].Acta Mathematicae Applicatae Sinica,1989,5(1):30-32.
Authors:Yongtai Ren  Li Han
Institution:1. North East Normal University, China
2. Liaoning Normal University, China
Abstract:This paper investigates the predator-prey system:

$$\begin{gathered}  \dot x = k_1 (x - \alpha x) - k(x)y, \hfill \\  \dot y = ( - k_s  + \beta k(x))y \hfill \\ \end{gathered}$$
Keywords:
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