Special Issue "Symmetry in Chaotic Systems and Circuits"

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Computer and Engineer Science and Symmetry".

Deadline for manuscript submissions: 30 September 2020.

Special Issue Editor

Prof. Dr. Christos Volos
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Guest Editor
Laboratory of Nonlinear Systems - Circuits & Complexity (LaNSCom), Department of Physics, Aristotle University of Thessaloniki, GR-54124 Thessaloniki, Greece
Interests: chaos; nonlinear circuits; nonlinear dynamics; chaotic cryptography
Special Issues and Collections in MDPI journals

Special Issue Information

Dear Colleagues,

Chaos theory is one of the most fascinating fields in modern science, revolutionizing our understanding of order and pattern in nature. Symmetry, a traditional and highly developed area of mathematics, would seem to lie at the opposite end of the spectrum. However, in the last few years, scientists have found connections between these two areas, connections which can have profound consequences for our understanding of the complex behavior in many physical, chemical, biological, and mechanical chaotic systems.

Therefore, symmetry can play an important role in the field of nonlinear systems and especially in the field of designing nonlinear circuits that produce chaos. In more detail, from designing chaotic systems and circuits with symmetric nonlinear terms to the study of system’s equilibria with symmetry in the case of self-excited attractors or symmetric line of equilibria in the case of hidden attractors, the feature of symmetry can play significant role in this kind of systems.

The aim of this Special Issue is to collect contributions in nonlinear chaotic systems and circuits that present as special a kind of symmetries as the aforementioned. Applications of chaotic systems and circuits where symmetry, or the deliberate lack of symmetry, is present, are also welcome.

Prof. Dr. Christos Volos
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • chaos
  • nonlinear systems
  • nonlinear circuits
  • control
  • synchronization
  • symmetric nonlinearities
  • self-excited attractors
  • hidden attractors
  • applications of chaotic systems and circuits with symmetries

Published Papers (9 papers)

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Research

Open AccessArticle
A Nonlinear Five-Term System: Symmetry, Chaos, and Prediction
Symmetry 2020, 12(5), 865; https://doi.org/10.3390/sym12050865 - 25 May 2020
Abstract
Chaotic systems have attracted considerable attention and been applied in various applications. Investigating simple systems and counterexamples with chaotic behaviors is still an important topic. The purpose of this work was to study a simple symmetrical system including only five nonlinear terms. We [...] Read more.
Chaotic systems have attracted considerable attention and been applied in various applications. Investigating simple systems and counterexamples with chaotic behaviors is still an important topic. The purpose of this work was to study a simple symmetrical system including only five nonlinear terms. We discovered the system’s rich behavior such as chaos through phase portraits, bifurcation diagrams, Lyapunov exponents, and entropy. Interestingly, multi-stability was observed when changing system’s initial conditions. Chaos of such a system was predicted by applying a machine learning approach based on a neural network. Full article
(This article belongs to the Special Issue Symmetry in Chaotic Systems and Circuits)
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Open AccessArticle
A Two-Parameter Modified Logistic Map and Its Application to Random Bit Generation
Symmetry 2020, 12(5), 829; https://doi.org/10.3390/sym12050829 - 18 May 2020
Abstract
This work proposes a modified logistic map based on the system previously proposed by Han in 2019. The constructed map exhibits interesting chaos related phenomena like antimonotonicity, crisis, and coexisting attractors. In addition, the Lyapunov exponent of the map can achieve higher values, [...] Read more.
This work proposes a modified logistic map based on the system previously proposed by Han in 2019. The constructed map exhibits interesting chaos related phenomena like antimonotonicity, crisis, and coexisting attractors. In addition, the Lyapunov exponent of the map can achieve higher values, so the behavior of the proposed map is overall more complex compared to the original. The map is then successfully applied to the problem of random bit generation using techniques like the comparison between maps, X O R , and bit reversal. The proposed algorithm passes all the NIST tests, shows good correlation characteristics, and has a high key space. Full article
(This article belongs to the Special Issue Symmetry in Chaotic Systems and Circuits)
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Open AccessFeature PaperArticle
Symmetry Evolution in Chaotic System
Symmetry 2020, 12(4), 574; https://doi.org/10.3390/sym12040574 - 05 Apr 2020
Cited by 1
Abstract
A comprehensive exploration of symmetry and conditional symmetry is made from the evolution of symmetry. Unlike other chaotic systems of conditional symmetry, in this work it is derived from the symmetric diffusionless Lorenz system. Transformation from symmetry and asymmetry to conditional symmetry is [...] Read more.
A comprehensive exploration of symmetry and conditional symmetry is made from the evolution of symmetry. Unlike other chaotic systems of conditional symmetry, in this work it is derived from the symmetric diffusionless Lorenz system. Transformation from symmetry and asymmetry to conditional symmetry is examined by constant planting and dimension growth, which proves that the offset boosting of some necessary variables is the key factor for reestablishing polarity balance in a dynamical system. Full article
(This article belongs to the Special Issue Symmetry in Chaotic Systems and Circuits)
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Open AccessArticle
A Novel Method for Performance Improvement of Chaos-Based Substitution Boxes
Symmetry 2020, 12(4), 571; https://doi.org/10.3390/sym12040571 - 05 Apr 2020
Cited by 2
Abstract
Symmetry plays an important role in nonlinear system theory. In particular, it offers several methods by which to understand and model the chaotic behavior of mathematical, physical and biological systems. This study examines chaotic behavior in the field of information security. A novel [...] Read more.
Symmetry plays an important role in nonlinear system theory. In particular, it offers several methods by which to understand and model the chaotic behavior of mathematical, physical and biological systems. This study examines chaotic behavior in the field of information security. A novel method is proposed to improve the performance of chaos-based substitution box structures. Substitution box structures have a special role in block cipher algorithms, since they are the only nonlinear components in substitution permutation network architectures. However, the substitution box structures used in modern block encryption algorithms contain various vulnerabilities to side-channel attacks. Recent studies have shown that chaos-based designs can offer a variety of opportunities to prevent side-channel attacks. However, the problem of chaos-based designs is that substitution box performance criteria are worse than designs based on mathematical transformation. In this study, a postprocessing algorithm is proposed to improve the performance of chaos-based designs. The analysis results show that the proposed method can improve the performance criteria. The importance of these results is that chaos-based designs may offer opportunities for other practical applications in addition to the prevention of side-channel attacks. Full article
(This article belongs to the Special Issue Symmetry in Chaotic Systems and Circuits)
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Open AccessFeature PaperArticle
A Symmetric Controllable Hyperchaotic Hidden Attractor
Symmetry 2020, 12(4), 550; https://doi.org/10.3390/sym12040550 - 04 Apr 2020
Cited by 2
Abstract
By introducing a simple feedback, a hyperchaotic hidden attractor is found in the newly proposed Lorenz-like chaotic system. Some variables of the equilibria-free system can be controlled in amplitude and offset by an independent knob. A circuit experiment based on Multisim is consistent [...] Read more.
By introducing a simple feedback, a hyperchaotic hidden attractor is found in the newly proposed Lorenz-like chaotic system. Some variables of the equilibria-free system can be controlled in amplitude and offset by an independent knob. A circuit experiment based on Multisim is consistent with the theoretic analysis and numerical simulation. Full article
(This article belongs to the Special Issue Symmetry in Chaotic Systems and Circuits)
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Open AccessArticle
Two New Asymmetric Boolean Chaos Oscillators with No Dependence on Incommensurate Time-Delays and Their Circuit Implementation
Symmetry 2020, 12(4), 506; https://doi.org/10.3390/sym12040506 - 01 Apr 2020
Cited by 1
Abstract
This manuscript introduces two new chaotic oscillators based on autonomous Boolean networks (ABN), preserving asymmetrical logic functions. That means that the ABNs require a combination of XOR-XNOR logic functions. We demonstrate analytically that the two ABNs do not have fixed points, and therefore, [...] Read more.
This manuscript introduces two new chaotic oscillators based on autonomous Boolean networks (ABN), preserving asymmetrical logic functions. That means that the ABNs require a combination of XOR-XNOR logic functions. We demonstrate analytically that the two ABNs do not have fixed points, and therefore, can evolve to Boolean chaos. Using the Lyapunov exponent’s method, we also prove the chaotic behavior, generated by the proposed chaotic oscillators, is insensitive to incommensurate time-delays paths. As a result, they can be implemented using distinct electronic circuits. More specifically, logic-gates–, GAL–, and FPGA–based implementations verify the theoretical findings. An integrated circuit using a CMOS 180nm fabrication technology is also presented to get a compact chaos oscillator with relatively high-frequency. Dynamical behaviors of those implementations are analyzed using time-series, time-lag embedded attractors, frequency spectra, Poincaré maps, and Lyapunov exponents. Full article
(This article belongs to the Special Issue Symmetry in Chaotic Systems and Circuits)
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Open AccessArticle
Image Encryption Algorithm Based on Tent Delay-Sine Cascade with Logistic Map
Symmetry 2020, 12(3), 355; https://doi.org/10.3390/sym12030355 - 01 Mar 2020
Cited by 3
Abstract
We propose a new chaotic map combined with delay and cascade, called tent delay-sine cascade with logistic map (TDSCL). Compared with the original one-dimensional simple map, the proposed map has increased initial value sensitivity and internal randomness and a larger chaotic parameter interval. [...] Read more.
We propose a new chaotic map combined with delay and cascade, called tent delay-sine cascade with logistic map (TDSCL). Compared with the original one-dimensional simple map, the proposed map has increased initial value sensitivity and internal randomness and a larger chaotic parameter interval. The chaotic sequence generated by TDSCL has pseudo-randomness and is suitable for image encryption. Based on this chaotic map, we propose an image encryption algorithm with a symmetric structure, which can achieve confusion and diffusion at the same time. Simulation results show that after encryption using the proposed algorithm, the entropy of the cipher is extremely close to the ideal value of eight, and the correlation coefficients between the pixels are lower than 0.01, thus the algorithm can resist statistical attacks. Moreover, the number of pixel change rate (NPCR) and the unified average changing intensity (UACI) of the proposed algorithm are very close to the ideal value, which indicates that it can efficiently resist chosen-plain text attack. Full article
(This article belongs to the Special Issue Symmetry in Chaotic Systems and Circuits)
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Open AccessArticle
Symmetric Key Encryption Based on Rotation-Translation Equation
Symmetry 2020, 12(1), 73; https://doi.org/10.3390/sym12010073 - 02 Jan 2020
Cited by 1
Abstract
In this paper, an improved encryption algorithm based on numerical methods and rotation–translation equation is proposed. We develop the new encryption-decryption algorithm by using the concept of symmetric key instead of public key. Symmetric key algorithms use the same key for both encryption [...] Read more.
In this paper, an improved encryption algorithm based on numerical methods and rotation–translation equation is proposed. We develop the new encryption-decryption algorithm by using the concept of symmetric key instead of public key. Symmetric key algorithms use the same key for both encryption and decryption. Most symmetric key encryption algorithms use either block ciphers or stream ciphers. Our goal in this work is to improve an existing encryption algorithm by using a faster convergent iterative method, providing secure convergence of the corresponding numerical scheme, and improved security by a using rotation–translation formula. Full article
(This article belongs to the Special Issue Symmetry in Chaotic Systems and Circuits)
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Open AccessArticle
New Chaotic Systems with Two Closed Curve Equilibrium Passing the Same Point: Chaotic Behavior, Bifurcations, and Synchronization
Symmetry 2019, 11(8), 951; https://doi.org/10.3390/sym11080951 - 26 Jul 2019
Cited by 2
Abstract
In this work, we introduce a chaotic system with infinitely many equilibrium points laying on two closed curves passing the same point. The proposed system belongs to a class of systems with hidden attractors. The dynamical properties of the new system were investigated [...] Read more.
In this work, we introduce a chaotic system with infinitely many equilibrium points laying on two closed curves passing the same point. The proposed system belongs to a class of systems with hidden attractors. The dynamical properties of the new system were investigated by means of phase portraits, equilibrium points, Poincaré section, bifurcation diagram, Kaplan–Yorke dimension, and Maximal Lyapunov exponents. The anti-synchronization of systems was obtained using the active control. This study broadens the current knowledge of systems with infinite equilibria. Full article
(This article belongs to the Special Issue Symmetry in Chaotic Systems and Circuits)
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Planned Papers

The below list represents only planned manuscripts. Some of these manuscripts have not been received by the Editorial Office yet. Papers submitted to MDPI journals are subject to peer-review.

Title: Dynamic Symmetry in Dozy-Chaos Mechanics
Authors: Vladimir V. Egorov
Affiliation: Russian Academy of Sciences, FSRC “Crystallography and Photonics”, Photochemistry Center, 7a Novatorov Street, Moscow 119421, Russian Federation

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