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Symmetry
Special Issues
Symmetry/Asymmetry in Chaos Theory and Application
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Symmetry/Asymmetry in Chaos Theory and Application

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

Deadline for manuscript submissions: 30 June 2025 | Viewed by 1962

Special Issue Editors

Prof. Dr. Chunbiao Li

E-Mail
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
Special Issues, Collections and Topics in MDPI journals
Dr. Eric Campos-Cantón

E-Mail Website
Co-Guest Editor
Division of Control and Dynamical Systems, Instituto Potosino Investigacion Cientifica y Tecnologica, 78216, SAN LUIS POTOSI, MEXICO
Interests: nonlinear and chaotic dynamics and their applications in science and engineering
Special Issues, Collections and Topics in MDPI journals
Dr. Sen Zhang

E-Mail Website
Co-Guest Editor
School of Artificial Intelligence, Nanjing University of Information Science and Technology, Nanjing 210044, China
Interests: memristive systems and circuits; chaotic systems; fractional-order chaotic systems and circuits; design and implementation of brain-like intelligent computing circuits based on memristors
Dr. Tengfei Lei

E-Mail Website
Co-Guest Editor
Collaborative Innovation Center of Memristive Computing Application (CICMCA), Qilu Institute of Technology, Jinan 250200, China
Interests: chaotic circuits and systems
Dr. Xudong Gao

E-Mail Website
Co-Guest Editor
School of Artificial Intelligence, Nanjing University of Information Science and Technology, Nanjing 210044, China
Interests: computational intelligence; nonlinear systems; control system design; power electronic circuits

Special Issue Information

Dear Colleagues,

Chaos theory, which studies the unpredictable yet deterministic behaviors of dynamic systems, often implies that slight changes in initial conditions generate vastly different outcomes. In recent years, chaos theory has made significant progress, including chaos regulation, the coexistence of chaos, chaotic multi-scroll attractors, chaos generated by special devices, neuromorphic chaos, and so on. Correspondingly, the application of chaos in different fields such as chaotic communication, encryption, chaotic stirring, and artificial intelligence is also developing in a promising direction.

However, the chaotic properties of a dynamic system are closely related to the structure of the system. Symmetric systems often output symmetric strange attractors, where broken symmetry is common, leading to coexisting pairs of attractors. Asymmetric systems often give asymmetric phase trajectories, which have great potential in terms of symmetry or conditional symmetry through the adjustment of feedback or based on offset boosting. Based on the observation of symmetry in a chaotic system, it is possible to establish an inherent connection between the topology and chaotic phase orbits, thus enabling a suitable selection of chaotic models with symmetry or asymmetry for practical applications.

By collecting research on the theoretical advancements of chaos, computational methods, and chaos-based practical applications, this Special Issue delves into the intricate balance between symmetry and asymmetry within all kinds of chaotic systems. The topics of this Special Issue comprise symmetric or asymmetric chaotic systems, including the corresponding applications such as secure communications, optimization algorithms, neural networks, brain-like computing, and artificial intelligence. By highlighting recent emerging trends of chaos, we aim to deepen our understanding and foster innovation by leveraging chaos theory for real-world applications.

Prof. Dr. Chunbiao Li
Guest Editor

Dr. Eric Campos Cantón
Dr. Sen Zhang
Dr. Tengfei Lei
Dr. Xudong Gao
Co-Guest Editors

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 submissions that pass pre-check are 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 2400 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

  • symmetric/asymmetric memristive systems
  • symmetric/asymmetric neural network
  • symmetric/asymmetric neurons
  • symmetric/asymmetric/conditional symmetric attractor
  • chaotic oscillation
  • symmetry broken
  • coexisting attractors
  • offset boosting
  • chaotic optimization algorithm
  • chaos application

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Published Papers (3 papers)

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Research

17 pages, 5536 KiB  
Article
A Simple Third-Order Hopfield Neural Network: Dynamic Analysis, Microcontroller Implementation and Application to Random Number Generation
by Victor Kamdoum Tamba, Viet-Thanh Pham and Christos Volos
Symmetry 2025, 17(3), 330; https://doi.org/10.3390/sym17030330 - 22 Feb 2025
Viewed by 318
Abstract
This manuscript introduces a simple third-order Hopfield neural network. Its dynamics, implementation with a microcontroller and application to random number generation are explored. The model includes three coupled neurons with no synaptic weights between the first neuron and the third, and between the [...] Read more.
This manuscript introduces a simple third-order Hopfield neural network. Its dynamics, implementation with a microcontroller and application to random number generation are explored. The model includes three coupled neurons with no synaptic weights between the first neuron and the third, and between the third and the second. The fundamental features (i.e., symmetry, dissipation and the requirement of existence of an attractor) of the model are studied. The results suggest that the model is asymmetric, dissipative and capable of supporting attractors. The dynamic analysis of the model is conducted through computer explorations, and the findings reveal that it develops complex behaviors like chaos and the coexistence of patterns. The coexistence of patterns is controlled using the linear augmentation method. The coexisting patterns are destroyed, and the multistable system is transformed into a monostable one. In order to confirm the numerical findings, a microcontroller implementation of the considered HNN model is carried out, and the findings of both approaches are concordant. Finally, the elaborated third-order HNN chaotic model is designed for random number generation application. The NIST statistical tests are provided in order to confirm the random features of the generated signals. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry in Chaos Theory and Application)
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23 pages, 11432 KiB  
Article
Chaos Regulation via Complex Nonlinear Feedback and Its Implementation Based on FPAA
by Jitong Xu, Chunbiao Li, Xiaoliang Cen, Xin Zhang and Lin Chai
Symmetry 2025, 17(2), 212; https://doi.org/10.3390/sym17020212 - 31 Jan 2025
Viewed by 458
Abstract
Complex nonlinear feedback is a key factor in the generation of chaos. In many cases, complex nonlinear functions have a higher probability for chaos producing, and correspondingly new bifurcations may be triggered in the dynamical system. Due to the difficulty in circuit implementation [...] Read more.
Complex nonlinear feedback is a key factor in the generation of chaos. In many cases, complex nonlinear functions have a higher probability for chaos producing, and correspondingly new bifurcations may be triggered in the dynamical system. Due to the difficulty in circuit implementation of complex nonlinear feedback, researchers often introduce simple nonlinear constraints to study the occurrence and evolution of chaos. In fact, the impact of complex nonlinear feedback on chaotic dynamics deserves further investigation. In this work, complex nonlinear feedback is introduced into an offset-boostable chaotic system as an example to observe and analyze its regulatory effect on the dynamics. Complex nonlinear feedback may destroy the property of symmetry of a system; therefore, we examine the evolution of chaotic attractors under the corresponding feedback and the functional transformation between bifurcation and non-bifurcation parameters as well. By fully utilizing the flexible configuration advantages of Field Programmable Analog Array (FPAA), arbitrary complex nonlinear functions are implemented to verify the chaotic dynamics. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry in Chaos Theory and Application)
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19 pages, 4102 KiB  
Article
On Fractional Discrete Memristive Model with Incommensurate Orders: Symmetry, Asymmetry, Hidden Chaos and Control Approaches
by Hussein Al-Taani, Ma’mon Abu Hammad, Mohammad Abudayah, Louiza Diabi and Adel Ouannas
Symmetry 2025, 17(1), 143; https://doi.org/10.3390/sym17010143 - 18 Jan 2025
Cited by 1 | Viewed by 750
Abstract
Memristives provide a high degree of non-linearity to the model. This property has led to many studies focusing on developing memristive models to provide more non-linearity. This article studies a novel fractional discrete memristive system with incommensurate orders using ϑi-th Caputo-like [...] Read more.
Memristives provide a high degree of non-linearity to the model. This property has led to many studies focusing on developing memristive models to provide more non-linearity. This article studies a novel fractional discrete memristive system with incommensurate orders using ϑi-th Caputo-like operator. Bifurcation, phase portraits and the computation of the maximum Lyapunov Exponent (LEmax) are used to demonstrate their impact on the system’s dynamics. Furthermore, we employ the sample entropy approach (SampEn), C0 complexity and the 0-1 test to quantify complexity and validate chaos in the incommensurate system. Studies indicate that the discrete memristive system with incommensurate fractional orders manifests diverse dynamical behaviors, including hidden chaos, symmetry, and asymmetry attractors, which are influenced by the incommensurate derivative values. Moreover, a 2D non-linear controller is presented to stabilize and synchronize the novel system. The work results are provided by numerical simulation obtained using MATLAB R2024a codes. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry in Chaos Theory and Application)
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