Carrying simplices in nonautonomous and random competitive Kolmogorov systems. (English) Zbl 1208.37009
Summary: The purpose of this paper is to investigate the asymptotic behavior of positive solutions of nonautonomous and random competitive Kolmogorov systems via the skew-product flows approach. It is shown that there exists an unordered carrying simplex which attracts all nontrivial positive orbits of the skew-product flow associated with a nonautonomous (random) competitive Kolmogorov system.
MSC:
| 37B55 | Topological dynamics of nonautonomous systems |
| 37H10 | Generation, random and stochastic difference and differential equations |
| 37N25 | Dynamical systems in biology |
| 92D25 | Population dynamics (general) |
| 34D05 | Asymptotic properties of solutions to ordinary differential equations |
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