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

Bocheng Liu, Jian Song, Niande Jiang () and Zhuo Wang
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Bocheng Liu: School of Information Engineering, Gandong University, Fuzhou 344000, 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

Mathematics, 2025, vol. 13, issue 14, 1-24

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.

Keywords: digital chaotic map; dynamic degradation; exponential delay feedback; logistic; Chebyshev (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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