Poisson stable motions of monotone nonautonomous dynamical systems

TL;DR

This paper investigates various forms of Poisson stability in monotone nonautonomous dynamical systems and solutions of related evolution equations, showing conditions under which trajectories converge to Poisson stable states.

Contribution

It provides a comprehensive analysis of Poisson stability types in monotone systems and establishes convergence of trajectories to these stable states under certain conditions.

Findings

Trajectories converge to Poisson stable states under specific conditions

Includes analysis for ODEs, FDEs, and parabolic PDEs

Extends stability concepts to a broad class of nonautonomous systems

Abstract

In this paper, we study the Poisson stability (in particular, stationarity, periodicity, quasi-periodicity, Bohr almost periodicity, almost automorphy, recurrence in the sense of Birkhoff, Levitan almost periodicity, pseudo periodicity, almost recurrence in the sense of Bebutov, pseudo recurrence, Poisson stability) of motions for monotone nonautonomous dynamical systems and of solutions for some classes of monotone nonautonomous evolution equations (ODEs, FDEs and parabolic PDEs). As a byproduct, some of our results indicate that all the trajectories of monotone systems converge to the above mentioned Poisson stable trajectories under some suitable conditions, which is interesting in its own right for monotone dynamics.