Weak Mixing in Switched Systems

TL;DR

This paper introduces and establishes the equivalence of various types of weakly mixing and Xiong chaotic sets in the context of switched systems, advancing the understanding of their dynamical properties.

Contribution

It defines new types of weakly mixing and Xiong chaotic sets for switched systems and proves their equivalence, providing a unified framework for analyzing chaos in such systems.

Findings

Weakly mixing sets of types 1, 2 are introduced.

Xiong chaotic sets of types 1, 2 are introduced.

The equivalence of these sets is established.

Abstract

Given a switched system, we introduce weakly mixing sets of type 1, 2 and Xiong chaotic sets of type 1, 2 with respect to a given set and show that they are equivalent respectively.