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An Exponentially Delayed Feedback Chaotic Model Resistant to Dynamic Degradation and Its Application

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  • Bocheng Liu

    (School of Information Engineering, Gandong University, Fuzhou 344000, China
    Jiangxi Institute of Industrial Technology for Internet of Things, Yingtan 335000, China)

  • Jian Song

    (School of Information Engineering, Gandong University, Fuzhou 344000, China)

  • Niande Jiang

    (School of Information Engineering, Gandong University, Fuzhou 344000, China)

  • Zhuo Wang

    (School of Computing Sciences, College of Computing-Informatics and Mathematics, Universiti Teknologi MARA, Shah Alam 40450, Malaysia
    School of Software, Nanchang University, Nanchang 330047, China)

Abstract

In this paper, an exponential delay feedback method is proposed to improve the performance of the digital chaotic maps against their dynamical degradation. In this paper, the performance of the scheme is verified using one-dimensional linear, exponential, and nonlinear exponential, Logistic, and Chebyshev maps, and numerical analyses show that the period during which the chaotic sequence enters the cycle is considerably prolonged, and the correlation performance is improved. At the same time, in order to verify the practicality of the method, an image encryption algorithm is designed, and its security analysis results show that the algorithm has a high level of security and can compete with other encryption schemes. Therefore, the exponential delay feedback method can effectively improve the dynamics degradation of a digital chaotic map.

Suggested Citation

  • Bocheng Liu & Jian Song & Niande Jiang & Zhuo Wang, 2025. "An Exponentially Delayed Feedback Chaotic Model Resistant to Dynamic Degradation and Its Application," Mathematics, MDPI, vol. 13(14), pages 1-24, July.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:14:p:2324-:d:1706702
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    References listed on IDEAS

    as
    1. Zhu, Hegui & Dai, Lewen & Liu, Yating & Wu, Lijun, 2021. "A three-dimensional bit-level image encryption algorithm with Rubik’s cube method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 185(C), pages 754-770.
    2. Yao Wu & Lingfeng Liu, 2020. "An Iteration-Time Combination Method to Reduce the Dynamic Degradation of Digital Chaotic Maps," Complexity, Hindawi, vol. 2020, pages 1-11, October.
    3. Shenli Zhu & Xiaoheng Deng & Wendong Zhang & Congxu Zhu, 2023. "Image Encryption Scheme Based on Newly Designed Chaotic Map and Parallel DNA Coding," Mathematics, MDPI, vol. 11(1), pages 1-22, January.
    4. Yue Zhu & Chunhua Wang & Jingru Sun & Fei Yu, 2023. "A Chaotic Image Encryption Method Based on the Artificial Fish Swarms Algorithm and the DNA Coding," Mathematics, MDPI, vol. 11(3), pages 1-18, February.
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