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 phase-translation group actions. The results are then applied to obtain global convergence of certain chemical reaction networks whose induced systems in reaction coordinates are monotone, as well as the dynamics of certain reaction-diffusion systems, in time-recurrent structure including periodicity, almost periodicity and almost automorphy. ∗Corresponding Author. Partially supported by NSF of China No.10971208, and the Finnish Center of Excellence in Analysis and Dynamics.