Hopf bifurcation analysis for a predator-prey system of Holling and Leslie type (Q1301995)
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scientific article; zbMATH DE number 1334890
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Hopf bifurcation analysis for a predator-prey system of Holling and Leslie type |
scientific article; zbMATH DE number 1334890 |
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Hopf bifurcation analysis for a predator-prey system of Holling and Leslie type (English)
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8 February 2000
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The authors study the Hopf bifurcation for the Holling-Tanner predator-prey model. Using Andronov-Hopf bifurcation theorem, they show that for some parameters the bifurcation is subcritical, i.e., there exists a small-amplitude repelling periodic orbit enclosing a stable equilibrium and separating it from another, stable limit cycle. The paper also summarizes earlier results of \textit{S.-B. Hsu} and \textit{T.-W. Hwang} [SIAM J. Appl. Math. 55, 763-783 (1995; Zbl 0832.34035)] on global asymptotical stability of the internal equilibrium.
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Holling-Tanner model
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predator-prey system
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Andronov-Hopf bifurcation
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multiple limit cycle
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0.9583219
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0.94824564
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0.94758236
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0.94747484
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0.9441639
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0.9425751
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