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Symmetry
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Symmetry in Chaos Theory and Applications
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Symmetry in Chaos Theory and Applications

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

Deadline for manuscript submissions: 30 June 2026 | Viewed by 1896

Special Issue Editors

Dr. Xiangliang Xu

E-Mail Website
Guest Editor
School of Information and Communication Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China
Interests: chaos theory and applications; chaotic system design; memristors; mobile robot; radar-jamming game-evolution technology
Dr. Guodong Li

E-Mail Website
Guest Editor
1. School of Mathematics and Computational Science, Guilin University of Electronic Technology, Guilin 541002, China
2. School of Mathematics and Computing Science, Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, Guilin University of Electronic Technology, Guilin 541002, China
3. Center for Applied Mathematics of Guangxi (GUET), Guilin 541002, China
Interests: Interests: fractals and chaos; chaotic system design; memristors; image–audio encryption algorithms; chaotic circuit design
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Tianxian Zhang

E-Mail Website
Guest Editor
School of Information and Communication Engineering, University of Electronic Science and Technology of China, Chengdu 610056, China
Interests: chaos theory and applications; mobile robot; radar-jamming game-evolution technology; multifunctional waveform design
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Symmetry plays a fundamental role in the modeling and analysis of chaotic and nonlinear systems. This Special Issue invites original research studies that explore how symmetry or asymmetry influences the dynamics, control, and applications of chaos in various systems, including memristor, multistability, and fractal and fractional-order models. 

Topics of interest include, but are not limited to, the following:

  1. Symmetry in nonlinear and chaotic systems;
  2. Memristor-based chaotic circuits and networks;
  3. Multistability and coexisting attractors;
  4. Fractal and fractional-order chaotic systems;
  5. Chaos-based encryption and secure communication;
  6. Symmetry breaking and bifurcation analysis;
  7. Control and synchronization of symmetric chaos;
  8. Applications in signal processing and computation. 

We welcome contributions from professionals in fields of mathematics, physics, computer science, and engineering.

We look forward to your contributions.

Dr. Xiangliang Xu
Dr. Guodong Li
Prof. Dr. Tianxian Zhang
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

  • symmetry in nonlinear and chaotic systems
  • memristor-based chaotic circuits and networks
  • multistability and coexisting attractors
  • fractal and fractional-order chaotic systems
  • chaos-based encryption and secure communication
  • symmetry breaking and bifurcation analysis
  • control and synchronization of symmetric chaos
  • applications in signal processing and computation

Benefits of Publishing in a Special Issue

  • Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
  • Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
  • External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
  • Reprint: MDPI Books provides the opportunity to republish successful Special Issues in book format, both online and in print.

Further information on MDPI's Special Issue policies can be found here.

Published Papers (3 papers)

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Research

21 pages, 1549 KB  
Article
Reinforcement Learning-Guided Particle Swarm Optimization for Multi-Objective Unmanned Aerial Vehicle Path Planning
by Wuke Li, Ying Xiong and Qi Xiong
Symmetry 2025, 17(8), 1292; https://doi.org/10.3390/sym17081292 - 11 Aug 2025
Viewed by 620
Abstract
Multi-objective Unmanned Aerial Vehicle (UAV) path planning in complex 3D environments presents a fundamental challenge requiring the simultaneous optimization of conflicting objectives such as path length, safety, altitude constraints, and smoothness. This study proposes a novel hybrid framework, termed QL-MOPSO, that integrates reinforcement [...] Read more.
Multi-objective Unmanned Aerial Vehicle (UAV) path planning in complex 3D environments presents a fundamental challenge requiring the simultaneous optimization of conflicting objectives such as path length, safety, altitude constraints, and smoothness. This study proposes a novel hybrid framework, termed QL-MOPSO, that integrates reinforcement learning with metaheuristic optimization through a three-stage hierarchical architecture. The framework employs Q-learning to generate a global guidance path in a discretized 2D grid environment using an eight-directional symmetric action space that embodies rotational symmetry at π/4 intervals, ensuring uniform exploration capabilities and unbiased path planning. A crucial intermediate stage transforms the discrete 2D path into a 3D initial trajectory, bridging the gap between discrete learning and continuous optimization domains. The MOPSO algorithm then performs fine-grained refinement in continuous 3D space, guided by a novel Q-learning path deviation objective that ensures continuous knowledge transfer throughout the optimization process. Experimental results demonstrate that the symmetric action space design yields 20.6% shorter paths compared to asymmetric alternatives, while the complete QL-MOPSO framework achieves 5% path length reduction and significantly faster convergence compared to standard MOPSO. The proposed method successfully generates Pareto-optimal solutions that balance multiple objectives while leveraging the symmetry-aware guidance mechanism to avoid local optima and accelerate convergence, offering a robust solution for complex multi-objective UAV path planning problems. Full article
(This article belongs to the Special Issue Symmetry in Chaos Theory and Applications)
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32 pages, 41108 KB  
Article
A Novel Medical Image Encryption Algorithm Based on High-Dimensional Memristor Chaotic System with Extended Josephus-RNA Hybrid Mechanism
by Yixiao Wang, Yutong Li, Zhenghong Yu, Tianxian Zhang and Xiangliang Xu
Symmetry 2025, 17(8), 1255; https://doi.org/10.3390/sym17081255 - 6 Aug 2025
Viewed by 440
Abstract
Conventional image encryption schemes struggle to meet the high security demands of medical images due to their large data volume, strong pixel correlation, and structural redundancy. To address these challenges, we propose a grayscale medical image encryption algorithm based on a novel 5-D [...] Read more.
Conventional image encryption schemes struggle to meet the high security demands of medical images due to their large data volume, strong pixel correlation, and structural redundancy. To address these challenges, we propose a grayscale medical image encryption algorithm based on a novel 5-D memristor chaotic system. The algorithm integrates a Symmetric L-type Josephus Spiral Scrambling (SLJSS) module and a Dynamic Codon-based Multi-RNA Diffusion (DCMRD) module to enhance spatial decorrelation and diffusion complexity. Simulation results demonstrate that the proposed method achieves near-ideal entropy (e.g., 7.9992), low correlation (e.g., 0.0043), and high robustness (e.g., NPCR: 99.62%, UACI: 33.45%) with time complexity of O(11MN), confirming its effectiveness and efficiency for medical image protection. Full article
(This article belongs to the Special Issue Symmetry in Chaos Theory and Applications)
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24 pages, 90648 KB  
Article
An Image Encryption Method Based on a Two-Dimensional Cross-Coupled Chaotic System
by Caiwen Chen, Tianxiu Lu and Boxu Yan
Symmetry 2025, 17(8), 1221; https://doi.org/10.3390/sym17081221 - 2 Aug 2025
Viewed by 549
Abstract
Chaotic systems have demonstrated significant potential in the field of image encryption due to their extreme sensitivity to initial conditions, inherent unpredictability, and pseudo-random behavior. However, existing chaos-based encryption schemes still face several limitations, including narrow chaotic regions, discontinuous chaotic ranges, uneven trajectory [...] Read more.
Chaotic systems have demonstrated significant potential in the field of image encryption due to their extreme sensitivity to initial conditions, inherent unpredictability, and pseudo-random behavior. However, existing chaos-based encryption schemes still face several limitations, including narrow chaotic regions, discontinuous chaotic ranges, uneven trajectory distributions, and fixed pixel processing sequences. These issues substantially hinder the security and efficiency of such algorithms. To address these challenges, this paper proposes a novel hyperchaotic map, termed the two-dimensional cross-coupled chaotic map (2D-CFCM), derived from a newly designed 2D cross-coupled chaotic system. The proposed 2D-CFCM exhibits enhanced randomness, greater sensitivity to initial values, a broader chaotic region, and a more uniform trajectory distribution, thereby offering stronger security guarantees for image encryption applications. Based on the 2D-CFCM, an innovative image encryption method was further developed, incorporating efficient scrambling and forward and reverse random multidirectional diffusion operations with symmetrical properties. Through simulation tests on images of varying sizes and resolutions, including color images, the results demonstrate the strong security performance of the proposed method. This method has several remarkable features, including an extremely large key space (greater than 2912), extremely high key sensitivity, nearly ideal entropy value (greater than 7.997), extremely low pixel correlation (less than 0.04), and excellent resistance to differential attacks (with the average values of NPCR and UACI being 99.6050% and 33.4643%, respectively). Compared to existing encryption algorithms, the proposed method provides significantly enhanced security. Full article
(This article belongs to the Special Issue Symmetry in Chaos Theory and Applications)
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