Phase-translation group actions on strongly monotone skew-product semiflows

We establish a convergence property for pseudo-bounded forward orbits of strongly monotone skew-product semiflows with invariant phasetranslation group actions. The results are then applied to obtain global convergence of certain chemical reaction networks whose associated systems in reaction coordinates are monotone, as well as the dynamics of certain reactiondiffusion systems in time-recurrent structure including periodicity, almost periodicity and almost automorphy.

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