Abstract:
This paper is dedicated to the study of the problem of existence of Poisson
stable (Bohr/Levitan almost periodic, almost automorphic, almost recurrent,
recurrent, pseudo-periodic, pseudo-recurrent and Poisson stable) motions of symmetric
monotone non-autonomous dynamical systems (NDS). It is proved that every
precompact motion of such system is asymptotically Poisson stable. We give also the
description of the structure of compact global attractor for monotone NDS with symmetry.
We establish the main results in the framework of general non-autonomous
(cocycle) dynamical systems. We apply our general results to the study of the problem
of existence of different classes of Poisson stable solutions and global attractors
for a chemical reaction network and nonautonomous translation-invariant difference
equations.