Dynamics of nonautonomous tridiagonal competitive–cooperative systems of differential equations

The skew-product flow which is generated by a nonautonomous recurrent tridiagonal competitive–cooperative system of differential equations is considered. It is shown that any minimal set is an almost 1-1 extension of the base flow and any ω-limit set contains at most two minimal sets, which generalizes the results of Smillie (1984 SIAM J. Math. Anal. 15 530–4) in autonomous cases and Smith (1991 SIAM J. Math. Anal. 22 1102–9) in time-periodic cases. Further results are also obtained in the case that the base flow is almost automorphic or almost periodic.

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