Advancing Chaos Theory: A Set-Valued Perspective on Multiple Mappings with Computational Detection Algorithms

TL;DR

This paper redefines Devaney chaos for multiple mappings using a set-valued approach and introduces computational algorithms to detect and visualize chaos, enabling exploration of complex dynamics in higher-dimensional systems.

Contribution

It presents a novel set-valued framework for analyzing chaos in multiple mappings and develops algorithms for detecting and visualizing chaotic behavior.

Findings

New conditions for chaos characterization in multiple mappings

Algorithms successfully detect and visualize chaos features

Validated theoretical concepts with computational tools

Abstract

This study redefines the analysis of Devaney chaos in multiple mappings from a set-valued perspective and introduces new conditions to characterize their chaotic behavior. As an innovative advancement, we develop computational algorithms to detect and visualize chaotic features such as transitivity and sensitivity. These algorithms provide tools to explore complex dynamics in higher-dimensional systems, validating theoretical concepts and opening new research avenues in chaos theory.