Chaotic Characteristics in Devaney’s Framework for Set-Valued Discrete Dynamical Systems

Abstract

This paper focuses on the relationship between a non-autonomous discrete dynamical system (NDDS) (H,f1,∞) and its induced set-valued discrete dynamical systems (K(H),f¯1,∞). Specifically, it explores the chaotic properties of these systems. The main finding is that f1,∞ is Devaney chaotic if and only if f¯1,∞ is Devaney chaotic in we-topology. The paper also provides similar conclusions for weak mixing, mixing, mild mixing, chain-transitivity, and chain-mixing in non-autonomous set-valued discrete dynamical systems (NSDDSs). Additionally, the paper proves that weak mixing implies sensitivity in NSDDSs.

Keywords

• Devaney chaos
• sensitivity
• set-valued discrete dynamical systems