Heteroclinic limit cycles in competitive Kolmogorov systems (Q379558)
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scientific article; zbMATH DE number 6224549
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Heteroclinic limit cycles in competitive Kolmogorov systems |
scientific article; zbMATH DE number 6224549 |
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Heteroclinic limit cycles in competitive Kolmogorov systems (English)
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11 November 2013
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Kolmogorov systems
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global attractors
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global repellers
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heteroclinic cycles
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A heteroclinic cycle is a closed curve that is topologically a circle consisting of fixed points and trajectories connecting them. The authors consider the Kolmogorov system NEWLINE\[NEWLINE\dot{x}_{i} = x_{i} f_{i}(x) , \,\, 1 \leq i \leq N.NEWLINE\]NEWLINE A notion of global attraction and repulsion of heteroclinic limit cycles is introduced. They obtain conditions for the existence of cycles linking the full set of axial equilibria and their global asymptotic behavior on the carrying simplex.
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