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Two-parameter bifurcation in a predator-prey system of Ivlev type. (English) Zbl 0894.34025
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 \[ a>-{2D+ (1-D)\log(1- D)\over D+(1- D)\log(1- D)} \log(1- D). \] .

34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
92D25 Population dynamics (general)
Full Text: DOI
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