Abstract
We consider a general time-dependent linear competitive-cooperative tridiagonal system of differential equations in the framework of skew-product flows and obtain canonical Floquet invariant bundles which are exponentially separated. Such Floquet bundles naturally reduce to the standard Floquet space when the system is assumed to be time-periodic. We apply the Floquet theory so obtained to study the dynamics on the hyperbolic omega-limit sets for the nonlinear competitive-cooperative tridiagonal systems in time-recurrent structures including almost periodicity and almost automorphy.
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