IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i21p3345-d1506463.html
   My bibliography  Save this article

Global Exponential Synchronization of Delayed Quaternion-Valued Neural Networks via Decomposition and Non-Decomposition Methods and Its Application to Image Encryption

Author

Listed:
  • Ramalingam Sriraman

    (Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur 603203, Tamil Nadu, India)

  • Ohmin Kwon

    (School of Electrical Engineering, Chungbuk National University, Cheongju 361763, Republic of Korea)

Abstract

With the rapid advancement of information technology, digital images such as medical images, grayscale images, and color images are widely used, stored, and transmitted. Therefore, protecting this type of information is a critical challenge. Meanwhile, quaternions enable image encryption algorithm (IEA) to be more secure by providing a higher-dimensional mathematical system. Therefore, considering the importance of IEA and quaternions, this paper explores the global exponential synchronization (GES) problem for a class of quaternion-valued neural networks (QVNNs) with discrete time-varying delays. By using Hamilton’s multiplication rules, we first decompose the original QVNNs into equivalent four real-valued neural networks (RVNNs), which avoids non-commutativity difficulties of quaternions. This decomposition method allows the original QVNNs to be studied using their equivalent RVNNs. Then, by utilizing Lyapunov functions and the matrix measure method (MMM), some new sufficient conditions for GES of QVNNs under designed control are derived. In addition, the original QVNNs are examined using the non-decomposition method, and corresponding GES criteria are derived. Furthermore, this paper presents novel results and new insights into GES of QVNNs. Finally, two numerical verifications with simulation results are given to verify the feasibility of the obtained criteria. Based on the considered master–slave QVNNs, a new IEA for color images Mandrill (256 × 256), Lion (512 × 512), Peppers (1024 × 1024) is proposed. In addition, the effectiveness of the proposed IEA is verified by various experimental analysis. The experiment results show that the algorithm has good correlation coefficients (CCs), information entropy (IE) with an average of 7.9988, number of pixels change rate (NPCR) with average of 99.6080%, and unified averaged changed intensity (UACI) with average of 33.4589%; this indicates the efficacy of the proposed IEAs.

Suggested Citation

  • Ramalingam Sriraman & Ohmin Kwon, 2024. "Global Exponential Synchronization of Delayed Quaternion-Valued Neural Networks via Decomposition and Non-Decomposition Methods and Its Application to Image Encryption," Mathematics, MDPI, vol. 12(21), pages 1-35, October.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:21:p:3345-:d:1506463
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/21/3345/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/21/3345/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Wei Feng & Xiangyu Zhao & Jing Zhang & Zhentao Qin & Junkun Zhang & Yigang He, 2022. "Image Encryption Algorithm Based on Plane-Level Image Filtering and Discrete Logarithmic Transform," Mathematics, MDPI, vol. 10(15), pages 1-24, August.
    2. Alsaedi, Ahmed & Cao, Jinde & Ahmad, Bashir & Alshehri, Ahmed & Tan, Xuegang, 2022. "Synchronization of master-slave memristive neural networks via fuzzy output-based adaptive strategy," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Gao, Suo & Iu, Herbert Ho-Ching & Mou, Jun & Erkan, Uğur & Liu, Jiafeng & Wu, Rui & Tang, Xianglong, 2024. "Temporal action segmentation for video encryption," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).
    2. Alexandru Dinu, 2024. "Singularity, Observability, and Independence: Unveiling Lorenz’s Cryptographic Potential," Mathematics, MDPI, vol. 12(18), pages 1-12, September.
    3. Shu, Jingsi & Zhang, Yongping, 2023. "Fractal control and synchronization of population competition model based on the T–S fuzzy model," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    4. Xue, Yu & Tu, Kairong & Liu, Chunyan & Zhang, Xian, 2024. "Non-fragile extended dissipative synchronization control for uncertain discrete-time neural networks with leakage and unbounded time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 185(C).
    5. Yang, Jinrong & Chen, Guici & Wen, Shiping & Wang, Leimin, 2023. "Finite-time dissipative control for discrete-time memristive neural networks via interval matrix method," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    6. Mingxu Wang & Xianping Fu & Xiaopeng Yan & Lin Teng, 2024. "A New Chaos-Based Image Encryption Algorithm Based on Discrete Fourier Transform and Improved Joseph Traversal," Mathematics, MDPI, vol. 12(5), pages 1-19, February.
    7. Zhang, Lingzhong & Lu, Jianquan & Jiang, Bangxin & Huang, Chi, 2023. "Distributed synchronization of delayed dynamic networks under asynchronous delay-dependent impulsive control," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:12:y:2024:i:21:p:3345-:d:1506463. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.