Non-permanence for Lotka-Volterra difference systems (Q2769770)
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scientific article; zbMATH DE number 1701933
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Non-permanence for Lotka-Volterra difference systems |
scientific article; zbMATH DE number 1701933 |
Statements
10 December 2002
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Lotka-Volterra difference systems
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permanent systems
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0.9320309
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0.92814666
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0.92679113
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0.91671365
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0.9143285
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0.9143166
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Non-permanence for Lotka-Volterra difference systems (English)
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The authors study the \(n\)-species Lotka-Volterra difference system NEWLINE\[NEWLINEx_i(k+1) = x_i(k) \exp{[r_i+\sum_{j=1}^n{a_{ij} x_j(k)}]}.NEWLINE\]NEWLINE They prove that if \(a_{ii}<0\) and \(a_{ij}>0\), \(i \neq j\), \(i,j=1, \ldots,n\), then such system is not permanent. This result extends a previous one given by \textit{Z. Lu} and \textit{W. Wang} [J. Math. Biol. 39, No.~3, 269-282 (1999; Zbl 0945.92022)] for two species.NEWLINENEWLINEFor the entire collection see [Zbl 0968.00066].
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