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Zbl 0894.34025
Sugie, Jitsuro
Two-parameter bifurcation in a predator-prey system of Ivlev type.
(English)
[J] J. Math. Anal. Appl. 217, No.2, 349-371 (1998). ISSN 0022-247X

This paper considers a predator-prey system of the form $$\dot x= rx(1- x)-(1- e^{-ax})y,\quad \dot y= y[(1- e^{-ax})- D],$$ where $D< 1-e^{-a}$, give a necessary and sufficient condition for the uniqueness of the limit cycle, which is $$a>-{2D+ (1-D)\log(1- D)\over D+(1- D)\log(1- D)} \log(1- D).$${}.
[Chen Lan Sun (Beijing)]
MSC 2000:
*34C05 Qualitative theory of some special solutions of ODE
92D25 Population dynamics

Keywords: predator-prey systems; limit cycles

Cited in: Zbl 1037.92029

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