THE PREDATOR-PREY MODEL WITH TWO LIMIT CYCLES

THE PREDATOR-PREY MODEL WITH TWO LIMIT CYCLES

This paper investigates the predator-prey system:x=k1（x-ax）-k（x）y,y=(-k3+βk（x）ywit.k（x）=k2x, x≤x, k2x, x>τ,where α, β, τ; k1, k2, k3 are positive constants.The main results are as follows（i） In case k3-βk2τ≥0 system （1） has no limit cycle.（ii） In case k3-βk2τ<0, k1+k3-βk2τ>0, an...

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Veröffentlicht in:Acta Mathematicae Applicatae Sinica 1989-03, Vol.5 (1), p.30-32
1. Verfasser: 任永泰 韩莉
Format: Artikel
Sprache:eng
Schlagworte:
constants
cycle
dividing
ending
erior
predator
singular
云一
五卜
子万
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Zusammenfassung:This paper investigates the predator-prey system:x=k1（x-ax）-k（x）y,y=(-k3+βk（x）ywit.k（x）=k2x, x≤x, k2x, x>τ,where α, β, τ; k1, k2, k3 are positive constants.The main results are as follows（i） In case k3-βk2τ≥0 system （1） has no limit cycle.（ii） In case k3-βk2τ<0, k1+k3-βk2τ>0, and for O<α<<1, system （1） at least has two limitcycles.
ISSN:0168-9673
1618-3932
DOI:10.1007/BF02006184