Special Issue "Symmetry in Chaotic Systems and Circuits Ⅱ"

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

Deadline for manuscript submissions: closed (30 November 2021).

Special Issue Editor

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 that 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 a 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 a significant role in such systems.

The aim of this Special Issue is to collect contributions considering nonlinear chaotic systems and circuits that present any of the aforementioned symmetries. 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 1800 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 (7 papers)

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Research

Article
Applicable Image Security Based on New Hyperchaotic System
Symmetry 2021, 13(12), 2290; https://doi.org/10.3390/sym13122290 - 01 Dec 2021
Viewed by 304
Abstract
Hyperchaotic systems are widely applied in the cryptography domain on account of their more complex dynamical behavior. In view of this, the greatest contribution of this paper is that a two-dimensional Sine coupling Logistic modulated Sine (2D-SCLMS) system is proposed based on Logistic [...] Read more.
Hyperchaotic systems are widely applied in the cryptography domain on account of their more complex dynamical behavior. In view of this, the greatest contribution of this paper is that a two-dimensional Sine coupling Logistic modulated Sine (2D-SCLMS) system is proposed based on Logistic map and Sine map. By a series of analyses, including Lyapunov index (LE), 0–1 test, two complexity analysis methods, and two entropy analysis methods, it is concluded that the new 2D-SCLMS map is hyperchaotic with a wider range of chaos and more complex randomness. The new system combined with two-dimensional Logistic-Sine Coupling Mapping (2D-LSCM) is further applied to an image encryption application. SHA-384 is used to generate the initial values and parameters of the two chaotic systems. Symmetric keys are generated during this operation, which can be applied to the proposed image encryption and decryption algorithms. The encryption process and the decryption process of the new image encryption approaches mainly include pixel scrambling, exclusive NOR (Xnor), and diffusion operations. Multiple experiments illustrate that this scheme has higher security and lower time complexity. Full article
(This article belongs to the Special Issue Symmetry in Chaotic Systems and Circuits Ⅱ)
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Article
Symmetric Oscillator: Special Features, Realization, and Combination Synchronization
Symmetry 2021, 13(11), 2142; https://doi.org/10.3390/sym13112142 - 10 Nov 2021
Viewed by 360
Abstract
Researchers have recently paid significant attention to special chaotic systems. In this work, we introduce an oscillator with different special features. In addition, the oscillator is symmetrical. The features and oscillator dynamics are discovered through different tools of nonlinear dynamics. An electronic circuit [...] Read more.
Researchers have recently paid significant attention to special chaotic systems. In this work, we introduce an oscillator with different special features. In addition, the oscillator is symmetrical. The features and oscillator dynamics are discovered through different tools of nonlinear dynamics. An electronic circuit is designed to mimic the oscillator’s dynamics. Moreover, the combined synchronization of two drives and one response oscillator is reported. Numerical examples illustrate the correction of our approach. Full article
(This article belongs to the Special Issue Symmetry in Chaotic Systems and Circuits Ⅱ)
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Article
The Dynamic Analysis of a Novel Reconfigurable Cubic Chaotic Map and Its Application in Finite Field
Symmetry 2021, 13(8), 1420; https://doi.org/10.3390/sym13081420 - 03 Aug 2021
Cited by 1 | Viewed by 423
Abstract
Dynamic degradation occurs when chaotic systems are implemented on digital devices, which seriously threatens the security of chaos-based pseudorandom sequence generators. The chaotic degradation shows complex periodic behavior, which is often ignored by designers and seldom analyzed in theory. Not knowing the exact [...] Read more.
Dynamic degradation occurs when chaotic systems are implemented on digital devices, which seriously threatens the security of chaos-based pseudorandom sequence generators. The chaotic degradation shows complex periodic behavior, which is often ignored by designers and seldom analyzed in theory. Not knowing the exact period of the output sequence is the key problem that affects the application of chaos-based pseudorandom sequence generators. In this paper, two cubic chaotic maps are combined, which have symmetry and reconfigurable form in the digital circuit. The dynamic behavior of the cubic chaotic map and the corresponding digital cubic chaotic map are analyzed respectively, and the reasons for the complex period and weak randomness of output sequences are studied. On this basis, the digital cubic chaotic map is optimized, and the complex periodic behavior is improved. In addition, a reconfigurable pseudorandom sequence generator based on the digital cubic chaotic map is constructed from the point of saving consumption of logical resources. Through theoretical and numerical analysis, the pseudorandom sequence generator solves the complex period and weak randomness of the cubic chaotic map after digitization and makes the output sequence have better performance and less resource consumption, which lays the foundation for applying it to the field of secure communication. Full article
(This article belongs to the Special Issue Symmetry in Chaotic Systems and Circuits Ⅱ)
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Article
Control of a Symmetric Chaotic Supply Chain System Using a New Fixed-Time Super-Twisting Sliding Mode Technique Subject to Control Input Limitations
Symmetry 2021, 13(7), 1257; https://doi.org/10.3390/sym13071257 - 13 Jul 2021
Cited by 8 | Viewed by 899
Abstract
Control of supply chains with chaotic dynamics is an important, yet daunting challenge because of the limitations and constraints there are in the amplitude of control efforts. In real-world systems, applying control techniques that need a large amplitude signal is impractical. In the [...] Read more.
Control of supply chains with chaotic dynamics is an important, yet daunting challenge because of the limitations and constraints there are in the amplitude of control efforts. In real-world systems, applying control techniques that need a large amplitude signal is impractical. In the literature, there is no study that considers the control of supply chain systems subject to control input limitations. To this end, in the current study, a new control scheme is proposed to tackle this issue. In the designed control input, limitations in control inputs, as well as robustness against uncertainties, are taken into account. The proposed scheme is equipped with a fixed time disturbance observer to eliminate the destructive effects of uncertainties and disturbances. Additionally, the super-twisting sliding mode technique guarantees the fixed-time convergence of the closed-loop system. After that, a symmetric supply chain system is presented, and its chaotic attractors are demonstrated. Finally, the proposed controller is applied to the symmetric supply chain system. Numerical simulations exhibit the proposed scheme’s excellent performance even though the system is subjected to control input limitations and time-varying uncertainties. Full article
(This article belongs to the Special Issue Symmetry in Chaotic Systems and Circuits Ⅱ)
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Article
FPGA Realization of the Parameter-Switching Method in the Chen Oscillator and Application in Image Transmission
Symmetry 2021, 13(6), 923; https://doi.org/10.3390/sym13060923 - 22 May 2021
Cited by 1 | Viewed by 679
Abstract
In this paper, the parameter-switching technique was applied to control chaos in the Chen oscillator and as a decryption mechanism in a secure transmission system, to transmit RGB and grayscale images. In the past few decades, considerable efforts have been put into the [...] Read more.
In this paper, the parameter-switching technique was applied to control chaos in the Chen oscillator and as a decryption mechanism in a secure transmission system, to transmit RGB and grayscale images. In the past few decades, considerable efforts have been put into the study of the stabilization of chaotic dynamical systems. Most of the well-known chaos control methods, such as Ott, Grebogi, and Yorke (OGY), Pyragas, and open-loop methods, force an unstable periodic orbit into a stable one while distorting the original attractor. On the other hand, the parameter-switching technique is an elegant method that can synthesize an already-existing stable orbit, thereby preserving the underlying attractor. Consequently, the main contributions of this work were the FPGA realizations of the parameter-switching method and a secure image transmission system using a synchronized master and slave topology. The results of the parameter-switching technique and synchronization were verified using phase plots and time series. The chaos-encrypted image from the image transmission system, verified using correlation, showed no relativity with the original image, while the recovery of the decrypted image has no loss of quality. The encryption and decryption system was symmetric, whereby the key was private. In this work, co-simulations were performed in Active-HDL with MATLAB/Simulink, while the target FPGA board was the Xilinx’s Artix-7 AC701. Full article
(This article belongs to the Special Issue Symmetry in Chaotic Systems and Circuits Ⅱ)
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Article
SIEA: Secure Image Encryption Algorithm Based on Chaotic Systems Optimization Algorithms and PUFs
Symmetry 2021, 13(5), 824; https://doi.org/10.3390/sym13050824 - 08 May 2021
Cited by 9 | Viewed by 864
Abstract
One of the general problems in modern digital society is undoubtedly the information security topic. It is critical to ensure the security of information transferred, processed, and stored throughout digital channels. Among this information, digital images draw attention in terms of frequency of [...] Read more.
One of the general problems in modern digital society is undoubtedly the information security topic. It is critical to ensure the security of information transferred, processed, and stored throughout digital channels. Among this information, digital images draw attention in terms of frequency of use in digital channels. In this study, a new image encryption algorithm is proposed to address the security problems of digital images. The aspect that differentiates the proposed algorithm from thousands of image encryption algorithms in the literature is that it is designed within the framework of the provable security design principle. The provable security design approach has ensured that the proposed algorithm is theoretically secure with mathematical proof techniques. In addition to addressing the proposed architecture security concerns, the hybrid random number generator used as the key generator constitutes another unique aspect. This generator, which was designed using chaotic systems, physical unclonable functions, and optimization algorithms, stands out as the innovative aspect of the study. The statistical randomness properties of the proposed random number generator were tested using the NIST SP 800-22 Statistical Test Suite. Successful results were obtained for 15 tests in the test package. In addition, the success of these outputs was tested on a new image encryption algorithm. The security of the proposed algorithm was tested from different angles using various experimental analyzes and a 12-step provable security analysis roadmap. Successful analysis results and performance measurements indicate that the proposed cryptographic components can be used in many information security applications and many future designs. Full article
(This article belongs to the Special Issue Symmetry in Chaotic Systems and Circuits Ⅱ)
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Article
Fractional-Order Analysis of Modified Chua’s Circuit System with the Smooth Degree of 3 and Its Microcontroller-Based Implementation with Analog Circuit Design
Symmetry 2021, 13(2), 340; https://doi.org/10.3390/sym13020340 - 19 Feb 2021
Cited by 2 | Viewed by 889
Abstract
In the paper, we futher consider a fractional-order system from a modified Chua’s circuit system with the smooth degree of 3 proposed by Fu et al. Bifurcation analysis, multistability and coexisting attractors in the the fractional-order modified Chua’s circuit are studied. In addition, [...] Read more.
In the paper, we futher consider a fractional-order system from a modified Chua’s circuit system with the smooth degree of 3 proposed by Fu et al. Bifurcation analysis, multistability and coexisting attractors in the the fractional-order modified Chua’s circuit are studied. In addition, microcontroller-based circuit was implemented in real digital engineering applications by using the fractional-order Chua’s circuit with the piecewise-smooth continuous system. Full article
(This article belongs to the Special Issue Symmetry in Chaotic Systems and Circuits Ⅱ)
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