Symmetry in Chaotic Systems and Circuits 2022

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

Deadline for manuscript submissions: closed (15 December 2022) | Viewed by 9912

Special Issue Editors


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Guest Editor
1. School of Artificial Intelligence, Nanjing University of Information Science & Technology, Nanjing 210044, China
2. Jiangsu Collaborative Innovation Center of Atmospheric Environment and Equipment Technology (CICAEET), Nanjing University of Information Science & Technology, Nanjing 210044, China
3. Collaborative Innovation Center of Memristive Computing Application (CICMCA), Qilu Institute of Technology, Jinan 250200, China
Interests: nonlinear circuits and systems; information and communication engineering
School of Electrical and Automation Engineering, East China Jiaotong University, Nanchang 330013, China
Interests: chaos theory and applications; memristive chaotic systems; multi-agent systems; complex network; deep learning
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Co-Guest Editor
Department of Mathematics, Shandong University, Weihai 264209, China
Interests: differential equations and dynamical systems
Special Issues, Collections and Topics in MDPI journals

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Co-Guest Editor
School of Electrical and Automation Engineering, Nanjing Normal University, Nanjing 210023, China
Interests: chaotic circuits and systems

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Co-Guest Editor
Collaborative Innovation Center of Memristive Computing Application (CICMCA), Qilu Institute of Technology, Jinan 250200, China
Interests: chaotic circuits and systems

Special Issue Information

Dear Colleagues,

Symmetry is a common phenomenon that exists widely in nonlinear circuits. Symmetric systems exhibit an elegant solution even when symmetry is broken. Symmetry can be obtained from various regimes of polarity balance, where reflection symmetry, rotational symmetry, and inversion symmetry are common in 3D systems and even offset boosting with a variable can return conditional symmetry. Symmetric chaotic circuits yield symmetric oscillation, which can be applied in many applications involving chaos-based engineering and has attracted great attention for study.

Many symmetric systems are robust, with global basin of attraction. When symmetry is broken, a symmetric pair of coexisting attractors may burst out, providing more possibilities with desired signal of bipolar and unipolar polarities. Chaotic systems of conditional symmetry provide extra alternatives for signal generation. In this sense, the design of symmetric chaotic circuits, including memristive circuits and neuron morphological circuits, is expected for meeting the requirements of more chaos-based applications. In this Special Issue, all new findings and reports on symmetric or conditional symmetric systems and circuits are welcome.

Prof. Dr. Chunbiao Li
Guest Editor

Prof. Dr. Qiang Lai
Prof. Dr. Xu Zhang
Prof. Dr. Fuhong Min
Dr. Tengfei Lei
Co-Guest Editors

Manuscript Submission Information

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Keywords

  • symmetry
  • conditional symmetry
  • offset boosting
  • chaotic circuit
  • memrisitve circuit
  • neuron morphological circuit

Published Papers (5 papers)

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Research

17 pages, 7764 KiB  
Article
Multiple Alternatives of Offset Boosting in a Symmetric Hyperchaotic Map
by Xizhai Ge, Chunbiao Li, Yongxin Li, Chuang Zhang and Changyuan Tao
Symmetry 2023, 15(3), 712; https://doi.org/10.3390/sym15030712 - 13 Mar 2023
Cited by 4 | Viewed by 3020
Abstract
The offset as the average value of a variable plays an important role in signal processing and system design. Offset boosting can be realized by a non-bifurcation parameter or an initial condition. In this work, symmetric coexisting attractors with opposite polarity and a [...] Read more.
The offset as the average value of a variable plays an important role in signal processing and system design. Offset boosting can be realized by a non-bifurcation parameter or an initial condition. In this work, symmetric coexisting attractors with opposite polarity and a 2D hyperchaotic map with multiple modes of offset boosting are proposed, where the offset can be controlled both by the initial condition and system parameter, and as a result, multiple alternatives of offset boosting and offset competition show up. Consequently, the final offset is determined eventually by the balance of two factors. The theoretical findings are verified through the hardware experiment based on the STM32. Finally, a pseudo-random number generator (PRNG) is constructed based on the newly proposed hyperchaotic map, demonstrating its high performance in engineering applications. Full article
(This article belongs to the Special Issue Symmetry in Chaotic Systems and Circuits 2022)
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9 pages, 3591 KiB  
Article
The Reappearance of Poetic Beauty in Chaos
by Suqiao Sheng, Huiyu Wen, Guangfu Xie and Yongxin Li
Symmetry 2022, 14(11), 2445; https://doi.org/10.3390/sym14112445 - 18 Nov 2022
Cited by 2 | Viewed by 1453
Abstract
Different forms of attractors, or basins of attraction, in chaotic systems often bring people the enjoyment of beauty. This attraction is reminiscent of ancient Chinese poetry and introduces people to a poetic and magical world, bringing them a sense of wonder and enlightenment. [...] Read more.
Different forms of attractors, or basins of attraction, in chaotic systems often bring people the enjoyment of beauty. This attraction is reminiscent of ancient Chinese poetry and introduces people to a poetic and magical world, bringing them a sense of wonder and enlightenment. In this work, some cases of the beauty of chaos, including forms of symmetry, asymmetry, conditional symmetry, and extension, are demonstrated. The chaos theory of science and engineering and the art of literature are innovatively combined and integrated here. The unique charm of chaotic attractors is revealed and endowed to the artistic realm of ancient Chinese poetry, helping people to understand the poetic beauty of the chaotic world. Through bold association and imagination, chaotic attractors are endowed with fresh vitality, thus showing people a world of artistic space that is full of fantasy. Full article
(This article belongs to the Special Issue Symmetry in Chaotic Systems and Circuits 2022)
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16 pages, 7754 KiB  
Article
Design and Implementation of Simplified Symmetry Chaotic Circuit
by Zhonglin Wang and Shutang Liu
Symmetry 2022, 14(11), 2299; https://doi.org/10.3390/sym14112299 - 2 Nov 2022
Cited by 3 | Viewed by 1145
Abstract
In order to reduce the circuit cost and improve the stability and flexibility of the circuit, a simplified symmetry chaotic circuit was designed and implemented by using an inverse integration circuit and a voltage follower as isolators. The change of different symmetry chaotic [...] Read more.
In order to reduce the circuit cost and improve the stability and flexibility of the circuit, a simplified symmetry chaotic circuit was designed and implemented by using an inverse integration circuit and a voltage follower as isolators. The change of different symmetry chaotic dynamic behaviors caused by the change of parameters can be realized by adjusting the time constant. The behavior coexistence characteristics and amplitude control characteristics under different initial conditions were verified. The results of circuit experiments are in good agreement with those of numerical simulation and theoretical analysis. This method is effective and feasible. Full article
(This article belongs to the Special Issue Symmetry in Chaotic Systems and Circuits 2022)
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18 pages, 5201 KiB  
Article
The Design of an Anti-Synchronization Control Algorithm for a 4D Laser System
by Zuoxun Wang, Jinhao Pan, Lei Ma and Guijuan Wang
Symmetry 2022, 14(4), 710; https://doi.org/10.3390/sym14040710 - 31 Mar 2022
Viewed by 1197
Abstract
When studying the control problems of nonlinear systems, there are always uncertainties and disturbances. The existence of this phenomenon will increase the error in production engineering and reduce work efficiency. In order to reduce the nonlinear asymmetric control, the control method of a [...] Read more.
When studying the control problems of nonlinear systems, there are always uncertainties and disturbances. The existence of this phenomenon will increase the error in production engineering and reduce work efficiency. In order to reduce the nonlinear asymmetric control, the control method of a laser hyperchaotic system is designed in this paper. The system is a complex number system, with remarkable nonlinear characteristics. The system is divided into two parts by calculating the state transformation matrix, which shows that the system can realize simultaneous synchronization and anti-synchronization. Firstly, in the ideal case, the stabilization, synchronization, and anti-synchronization of the system are studied by using the dynamic gain feedback method, and a dynamic feedback controller is designed. Secondly, in the case of uncertainty and disturbance, a dynamic feedback control strategy based on uncertainty and disturbance estimator (UDE) is proposed. With the aim to solve the control problem of the system, the corresponding controller is designed to modify the system. Finally, through simulation and comparison, it is verified that the effect of this method is remarkable. Full article
(This article belongs to the Special Issue Symmetry in Chaotic Systems and Circuits 2022)
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17 pages, 2931 KiB  
Article
Complete Synchronization and Partial Anti-Synchronization of Complex Lü Chaotic Systems by the UDE-Based Control Method
by Zuoxun Wang, Cong Song, An Yan and Guijuan Wang
Symmetry 2022, 14(3), 517; https://doi.org/10.3390/sym14030517 - 2 Mar 2022
Cited by 10 | Viewed by 1821
Abstract
The presence of uncertainty and disturbance can lead to asymmetric control of nonlinear systems, and this asymmetric control can lead to a decrease in the productivity of the engineered system. In order to improve the control speed of the improved nonlinear system, complete [...] Read more.
The presence of uncertainty and disturbance can lead to asymmetric control of nonlinear systems, and this asymmetric control can lead to a decrease in the productivity of the engineered system. In order to improve the control speed of the improved nonlinear system, complete synchronization and partial anti-synchronization of complex Lü chaotic systems with uncertainty and disturbance are investigated in the present paper. First, a new UDE-based dynamic feedback control method is proposed for the complete synchronization problem of the system. The method unites the dynamic gain feedback control method and the uncertainty and perturbation estimator (UDE) control method, where the dynamic gain feedback controller is used to achieve asymptotic stability of the nominal system and the UDE controller is used to handle a given controlled system with uncertainty and disturbance. Second, for the partial desynchronization problem of this system, a new UDE-based linear-like feedback control method is proposed, which consists of two controllers: a linear-like feedback controller used to achieve the asymptotic stabilization of the nominal system and the other UDE controller is designed to handle the given controlled system with uncertainty and disturbance. Finally, numerical simulations are performed to verify the correctness and stability of the theoretical results. Full article
(This article belongs to the Special Issue Symmetry in Chaotic Systems and Circuits 2022)
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