Stable oscillations in a predator-prey model with time lag (Q5903488)
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scientific article; zbMATH DE number 4027250
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Stable oscillations in a predator-prey model with time lag |
scientific article; zbMATH DE number 4027250 |
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Stable oscillations in a predator-prey model with time lag (English)
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1988
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The Lotka-Volterra model with a time delay in the interspecies interaction terms is considered. The time delay is modelled by an integral with the weight kernel aexp(-at). It is shown that under certain conditions imposed upon the parameters of the system a supercritical Hopf bifurcation takes place at a certain value \(a_ 0\) of ``a'' and the bifurcating closed periodic paths are orbitally asymptotically stable for values of ``a'' below \(a_ 0\).
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equilibrium points
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center manifold
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Lotka-Volterra model
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time delay
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interspecies interaction terms
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supercritical Hopf bifurcation
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bifurcating closed periodic paths
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orbitally asymptotically stable
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