Geometric approach for global asymptotic stability of three-dimensional Lotka-Volterra systems (Q663732)
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scientific article; zbMATH DE number 6009684
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Geometric approach for global asymptotic stability of three-dimensional Lotka-Volterra systems |
scientific article; zbMATH DE number 6009684 |
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Geometric approach for global asymptotic stability of three-dimensional Lotka-Volterra systems (English)
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27 February 2012
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The authors treat \(n\)-dimensional Lotka-Volterra systems with a unique positive equilibrium \(E\). They discuss several known conjectures on global asymptotic stability and prove an interesting result concerning the global asymptotic stability of \(E\) in the case \(n=3\). For the proof, they use the so-called geometric approach and earlier results by Li and Muldowney, involving the Lozinskii measure and time average properties derived by Hofbauer and Sigmund.
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Lotka-Volterra system
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global asymptotic stability
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geometric approach
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time average
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