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THE UNIQUENESS OF THE LIMIT CLYCLES OF PREDATOR-PREY SYSTEM(A1) WITH THE PREDATOR'S FUNCTIONALRESPONSE OBEYING THE THIRD KINDOF HOLLING CURVE
Xiong Wiemin
1986, 5(2):
42-50.
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.
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