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.
