On the \({\omega}\)-limit set dichotomy of cooperating Kolmogorov systems (Q1417874)
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scientific article; zbMATH DE number 2021985
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the \({\omega}\)-limit set dichotomy of cooperating Kolmogorov systems |
scientific article; zbMATH DE number 2021985 |
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On the \({\omega}\)-limit set dichotomy of cooperating Kolmogorov systems (English)
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6 January 2004
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The authors study cooperative systems of the form \[ x'_i=x_i f(x), \quad x_i\geq 0, \quad i=1,\dots, n. \] They investigate the following property of \(\omega\)-limit sets: if \(x<y\) (in the sense of usual order on the positive orthant), then either \(\omega(x)\leq \omega(y)\) or \(\omega(x)=\omega(y)\subset E\), where \(E\) is the set of equilibria.
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cooperative systems
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\(\omega\)-limit set
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irreducible
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convergence
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equilibrium
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