Editorial

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3 pages, 160 KiB

Open AccessEditorial

Symmetry in Chaotic Systems and Circuits II

by Christos Volos

Symmetry 2022, 14(8), 1651; https://0-doi-org.brum.beds.ac.uk/10.3390/sym14081651 - 10 Aug 2022

Viewed by 619

Abstract

Today, one of the most studied phenomena of nonlinear dynamical systems is Chaos [...] Full article

(This article belongs to the Special Issue Symmetry in Chaotic Systems and Circuits Ⅱ)

Research

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14 pages, 6571 KiB

Open AccessArticle

A Chaotic Quadratic Oscillator with Only Squared Terms: Multistability, Impulsive Control, and Circuit Design

by Dhinakaran Veeman, Ahmad Alanezi, Hayder Natiq, Sajad Jafari and Ahmed A. Abd El-Latif

Symmetry 2022, 14(2), 259; https://0-doi-org.brum.beds.ac.uk/10.3390/sym14020259 - 28 Jan 2022

Cited by 6 | Viewed by 1948

Abstract

Here, a chaotic quadratic oscillator with only squared terms is proposed, which shows various dynamics. The oscillator has eight equilibrium points, and none of them is stable. Various bifurcation diagrams of the oscillator are investigated, and its Lyapunov exponents (LEs) are discussed. The [...] Read more.

Here, a chaotic quadratic oscillator with only squared terms is proposed, which shows various dynamics. The oscillator has eight equilibrium points, and none of them is stable. Various bifurcation diagrams of the oscillator are investigated, and its Lyapunov exponents (LEs) are discussed. The multistability of the oscillator is discussed by plotting bifurcation diagrams with various initiation methods. The basin of attraction of the oscillator is discussed in two planes. Impulsive control is applied to the oscillator to control its chaotic dynamics. Additionally, the circuit is implemented to reveal its feasibility. Full article

(This article belongs to the Special Issue Symmetry in Chaotic Systems and Circuits Ⅱ)

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25 pages, 16290 KiB

Open AccessArticle

Applicable Image Security Based on New Hyperchaotic System

by Jingya Wang, Xianhua Song, Huiqiang Wang and Ahmed A. Abd El-Latif

Symmetry 2021, 13(12), 2290; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13122290 - 01 Dec 2021

Cited by 7 | Viewed by 1466

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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12 pages, 960 KiB

Open AccessArticle

Symmetric Oscillator: Special Features, Realization, and Combination Synchronization

by Victor Kamdoum Tamba, Janarthanan Ramadoss, Viet-Thanh Pham, Giuseppe Grassi, Othman Abdullah Almatroud and Iqtadar Hussain

Symmetry 2021, 13(11), 2142; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13112142 - 10 Nov 2021

Cited by 4 | Viewed by 1652

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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24 pages, 31601 KiB

Open AccessArticle

The Dynamic Analysis of a Novel Reconfigurable Cubic Chaotic Map and Its Application in Finite Field

by Chuanfu Wang, Yi Di, Jianyu Tang, Jing Shuai, Yuchen Zhang and Qi Lu

Symmetry 2021, 13(8), 1420; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13081420 - 03 Aug 2021

Cited by 10 | Viewed by 1616

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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15 pages, 4525 KiB

Open AccessArticle

Control of a Symmetric Chaotic Supply Chain System Using a New Fixed-Time Super-Twisting Sliding Mode Technique Subject to Control Input Limitations

by Bo Wang, Hadi Jahanshahi, Christos Volos, Stelios Bekiros, Abdullahi Yusuf, Praveen Agarwal and Ayman A. Aly

Symmetry 2021, 13(7), 1257; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13071257 - 13 Jul 2021

Cited by 25 | Viewed by 2875

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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21 pages, 2470 KiB

Open AccessArticle

FPGA Realization of the Parameter-Switching Method in the Chen Oscillator and Application in Image Transmission

by Vincent-Ademola Adeyemi, Jose-Cruz Nuñez-Perez, Yuma Sandoval Ibarra, Francisco-Javier Perez-Pinal and Esteban Tlelo-Cuautle

Symmetry 2021, 13(6), 923; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13060923 - 22 May 2021

Cited by 8 | Viewed by 2590

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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21 pages, 9314 KiB

Open AccessArticle

SIEA: Secure Image Encryption Algorithm Based on Chaotic Systems Optimization Algorithms and PUFs

by Aina’u Shehu Muhammad and Fatih Özkaynak

Symmetry 2021, 13(5), 824; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13050824 - 08 May 2021

Cited by 26 | Viewed by 3404

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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13 pages, 5244 KiB

Open AccessArticle

Fractional-Order Analysis of Modified Chua’s Circuit System with the Smooth Degree of 3 and Its Microcontroller-Based Implementation with Analog Circuit Design

by Junxia Wang, Li Xiao, Karthikeyan Rajagopal, Akif Akgul, Serdar Cicek and Burak Aricioglu

Symmetry 2021, 13(2), 340; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13020340 - 19 Feb 2021

Cited by 16 | Viewed by 2671

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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