Combining chaotic dynamical systems using the fuzzy logic XOR operator

Rezki Chemlal; Hacene Gharout

doi:10.2478/gm-2025-0004

.blurhash-client-img { display: none !important; }

Combining chaotic dynamical systems using the fuzzy logic XOR operator

General Mathematics

Volume 33 (2025): Issue 1 (June 2025)

By: Rezki Chemlal and Hacene Gharout

Open Access

|Apr 2026

Abstract

In this paper we explore whatever combining two chaotic dynamical systems using the fuzzy logic operator XOR can maintain or not the chaotic properties of the resulting dynamical system. This study is motivated by techniques used in applications to secure communications and cryptography.

References

M. S. Baptista, Cryptography with chaos, Physics Letters A., vol. 240, no. 1-2, 1998, 50-54.
Search in Google Scholar Back to article
R. Chemlal, I. Djellit, oding Information and Problems of storage in Dynamical Systems, FACTA UNIVERSITATIS, SER ELEC ENERG, vol. 17, December, 2004, 355-363.
Search in Google Scholar Back to article
A. S. Dmitriev, Storing and Recognizing Information with One-Dimensional Dynamic Systems, (In Russian), Radiotechnika i Elektrononika, vol. 36, no. 1, 1991, 101-108.
Search in Google Scholar Back to article
A. A. Dmitriev, Design of message-carrying chaotic sequences, Nonlinear Phenomena in Complex Systems, vol. 5, no. 1, 2002, 78-83.
Search in Google Scholar Back to article
H. K. Kwan, Three-layer bidirectional asymmetrical associative memory, Proceedings of the 2003 International Symposium on Circuits and Systems, 2003. ISCAS ’03., Bangkok, Thailand, doi: 10.1109/ISCAS.2003.1205061.
Search in Google Scholar Back to article
L. Kocarev, Chaos-based cryptography: a brief overview, in IEEE Circuits and Systems Magazine, vol. 1, no. 3, 2001, 6-21.
Search in Google Scholar Back to article
M. Kushnir, Y. Fedkovych, P. Kroialo, H. Kosovan, Encryption of the Images on the Basis of Two Chaotic Systems with the Use of Fuzzy Logic, IEEE 15 th International Conference on Advanced Trends in Radioelectronics, Telecommunications and Computer Engineering (TCSET), 2020.
Search in Google Scholar Back to article
S. Mokhnache, M. E. H. Daachi, T. Bekkouche, N. Diffellah, A Combined Chaotic System for Speech Encryption, Eng. Technol. Appl. Sci. Res., vol. 12, no. 3, 2022, 8578-8583.
Search in Google Scholar Back to article
N. K. Pareek, V. Patidar, Cryptography using multiple one-dimensional chaotic maps, Communications in Nonlinear Science and Numerical Simulation, vol. 10, no. 7, 2005, 715-723.
Search in Google Scholar Back to article
S. Rouabhi, Storage of Information in One Dimensional Piecewise Continuous Maps, International Journal of Bifurcation and Chaos, vol. 10, no. 5, 2000, 1127-1137.
Search in Google Scholar Back to article
S. Luzzatto, Introduction to smooth ergodic theory, Abdus Salam International Centre for Theoretical Physics Trieste, Italy, 2013, https://indico.ictp.it/event/a12289/session/2/contribution/1/material/0/0.pdf
Search in Google Scholar Back to article
P. G. Vaidya, S. Angadi, Decoding chaotic cryptography without access to the superkey, Chaos, Solitons and Fractals, vol. 17, no. 2-3,2003, 379-386.
Search in Google Scholar Back to article
M. Vellekoop, R. Berglund, On intervals, transitivity = chaos, The American Mathematical Monthly, Taylor and Francis, vol. 101, no. 4, 1994, 353-355.
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.2478/gm-2025-0004 | Journal eISSN: 1584-3289 | Journal ISSN: 1221-5023

Journal RSS Feed

Language: English

Page range: 51 - 63

Submitted on: Oct 1, 2024

Accepted on: May 11, 2025

Published on: Apr 8, 2026

Published by: Lucian Blaga University of Sibiu

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

Chaos,

Related subjects:

Differential equations and dynamical systems,

Probability and statistics,

Numerical and computational mathematics,

Applied mathematics

© 2026 Rezki Chemlal, Hacene Gharout, published by Lucian Blaga University of Sibiu
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 33 (2025): Issue 1 (June 2025)