Dynamics of the periodic type-K competitive Kolmogorov systems |
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Authors: | Mats Gyllenberg |
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Institution: | a Department of Mathematics and Statistics, University of Helsinki, FIN-00014 Helsinki, Finland b Department of Mathematics, University of Turku, FIN-20014 Turku, Finland |
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Abstract: | For time-periodic dissipative and irreducible type-K competitive Kolmogorov systems, it is proved that there is a canonically defined countable family F of unordered, disjoint invariant sets with the property that, for every persistent trajectory whose ω-limit set is not a cycle, there exists a unique trajectory in some element of F such that these two trajectories are asymptotic and the corresponding points in these two trajectories are K-related. |
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Keywords: | Time-periodic type-K competitive system Poincaré map Persistence Invariant order decomposition Exponential separation Pesin's theory |
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