A CMOS Tailed Tent Map for the Generation of Uniformly Distributed Chaotic Sequences

TL;DR

This paper introduces a modified CMOS tailed tent map that generates uniformly distributed chaotic sequences, overcoming parasitic equilibrium issues and maintaining statistical properties with robust parameter deviations.

Contribution

The paper presents a novel tailed tent map design that ensures uniform chaotic sequences and robustness, addressing limitations of traditional tent maps and Bernoulli shift circuits.

Findings

The proposed map maintains uniform distribution despite parameter variations.

It avoids parasitic stable equilibria that hinder chaos in traditional maps.

The circuit demonstrates improved robustness and statistical reliability.

Abstract

This paper describes the design of a modified tent map characterized by a uniform probability density function. The use of this map is proposed as an alternative to the tent map and the Bernoulli shift. It is shown that practical circuits implementing the latter two maps may possess parasitic stable equilibria, fact which would prevent the desired chaotic behavior of the system. On the other hand, commonly used strategies to avoid the parasitic equilibria onset also affect the uniformity of the probability density function. Conversely, the use of the proposed tailed tent map allows to assure a certain degree of parameter deviation robustness, without compromising on the statistical properties of the system.