Two-parameter bifurcation in a predator-prey system of Ivlev type (Q1378629)
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scientific article; zbMATH DE number 1115475
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Two-parameter bifurcation in a predator-prey system of Ivlev type |
scientific article; zbMATH DE number 1115475 |
Statements
Two-parameter bifurcation in a predator-prey system of Ivlev type (English)
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7 September 1998
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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 \[ a>-{2D+ (1-D)\log(1- D)\over D+(1- D)\log(1- D)} \log(1- D). \] {}.
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predator-prey systems
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limit cycles
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