Abstract: In this paper,we consider the Predator-Prey system(A₁) that the predator's functional response obeys the third kind of Holling Curve s=r(1-s/K)s-(as²x/(1+bs²)≡as²/(1+bs²)[f(s)-x], x=x(ms²/(1+bs²)-D₀)≡(m-D₀b)x/(1+bs²)(s²-β²)·(A₁), f(s)=(r/as)((1-s)/K)(1+bs²), β=√D₀/m-D₀b, s₍₀₎=s₀>0,x₍₀₎=x₀>0,K,r,a,b,m,D₀ are all positive const. We have proved that If f'(β)>0, then there is the unique limit cycles of the Predator-Prey system (A₁) in s>0,x>0.

摘要： 本文用与[5]证明Liénard方程极限环唯一性类似的方法,证明了食饵具有x线性密度制约,捕食者只有Holling第三类功能性反应的捕食者——食饵系统<A₁>, s=(as²)/(1+bs²)[f(s)-x], x=(m-D₀b)(x)/1+bs²)[s²-β²]·<A₁>其中:f(s)=(r/as)(1-s/K)(1+bs²), β=√D₀/m-D₀b, s₍₀₎=s₀>0,x₍₀₎=x₀>0,K.r.a.b.m.D₀均为正常数若f'(β)>0,则在s>0,x>0内存在唯一的极限环。