Dynamics of the periodic type-\(K\) competitive Kolmogorov systems (Q1887550)

The author considers a class of time-periodic dissipative and irreducible type-K competitive Kolmogorov systems. It is proved that there is a canonically defined countable family \({\mathcal F}\) of unordered, disjoint invariant sets with the property that for every persistent trajectory whose \(\omega\)-limit set is not a cycle, there exists a unique trajectory in some element of \({\mathcal F}\) such that these two trajectories are asymptotic and the corresponding points in these two trajectories are \(K\)-related.