Devaney chaos in non-autonomous discrete systems

TL;DR

This paper investigates Devaney chaos in non-autonomous discrete systems, establishing conditions under which transitivity and density of periodic points imply sensitivity, and explores chaotic behavior in systems governed by convergent sequences of maps.

Contribution

It provides new conditions linking chaos components in non-autonomous systems and analyzes chaos in systems driven by convergent sequences of continuous maps.

Findings

Transitivity and density imply sensitivity in unbounded sets.

Additional conditions are needed for bounded sets.

Chaotic behavior occurs in systems with convergent map sequences.

Abstract

This paper is concerned with Devaney chaos in non-autonomous discrete systems. It is shown that in its definition, the two former conditions, i.e., transitivity and density of periodic points, in a set imply the last one, i.e., sensitivity, in the case that the set is unbounded, while a similar result holds under two additional conditions in the other case that the set is bounded. Furthermore, some chaotic behavior is studied for a class of non-autonomous systems, each of which is governed by a convergent sequence of continuous maps.