Theoretical design and circuit implementation of integer domain chaotic systems

TL;DR

This paper introduces a new method for designing integer domain chaotic systems, proves their chaotic behavior mathematically, and implements them in an analog-digital hybrid circuit, validated through experiments.

Contribution

It presents a novel systematic approach for constructing and implementing integer domain chaotic systems with experimental validation.

Findings

Mathematically proven chaos according to Devaney's definition.

Successful realization of IDCS in an analog-digital hybrid circuit.

Experimental results validate the proposed design methodology.

Abstract

In this paper, a new approach for constructing integer domain chaotic systems (IDCS) is proposed, and its chaotic behavior is mathematically proven according to the Devaney's definition of chaos. Furthermore, an analog-digital hybrid circuit is also developed for realizing the designed basic IDCS. In the IDCS circuit design, chaos generation strategy is realized through a sample-hold circuit and a decoder circuit so as to convert the uniform noise signal into a random sequence, which plays a key role in circuit implementation. The experimental observations further validate the proposed systematic methodology for the first time.