中国物理B ›› 2025, Vol. 34 ›› Issue (9): 90504-090504.doi: 10.1088/1674-1056/adea5c

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Design of a memristive chaotic map and its adaptive regulation

Ya Wang(王亚)1, Xin-Lin Song(宋欣林)2,†, and Fei-Fei Yang(杨飞飞)3   

  1. 1 School of Cyber Security, Gansu University of Political Science and Law, Lanzhou 730070, China;
    2 College of Science, Xi'an University of Science and Technology, Xi'an 710054, China;
    3 College of Artificial Intelligence and Computer Science, Xi'an University of Science and Technology, Xi'an 710054, China
  • 收稿日期:2025-05-18 修回日期:2025-06-18 接受日期:2025-07-01 出版日期:2025-08-21 发布日期:2025-09-22
  • 通讯作者: Xin-Lin Song E-mail:xinlinsong@xust.edu.cn
  • 基金资助:
    memristive map|dynamic performance|adaptive regulation of energy

Design of a memristive chaotic map and its adaptive regulation

Ya Wang(王亚)1, Xin-Lin Song(宋欣林)2,†, and Fei-Fei Yang(杨飞飞)3   

  1. 1 School of Cyber Security, Gansu University of Political Science and Law, Lanzhou 730070, China;
    2 College of Science, Xi'an University of Science and Technology, Xi'an 710054, China;
    3 College of Artificial Intelligence and Computer Science, Xi'an University of Science and Technology, Xi'an 710054, China
  • Received:2025-05-18 Revised:2025-06-18 Accepted:2025-07-01 Online:2025-08-21 Published:2025-09-22
  • Contact: Xin-Lin Song E-mail:xinlinsong@xust.edu.cn

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摘要： The analysis of structure and dynamics in chaotic systems has long been a significant research direction in nonlinear science. Constructing a reliable chaotic system with rich dynamical characteristics is essential for secure communication applications. Existing memristor-based chaotic maps are typically obtained by incorporating discrete mathematical models of memristors into basic chaotic maps. In this study, a simple memristive nonlinear circuit is first designed, from which a memristive oscillator is derived. Subsequently, a memristive map is developed from this oscillator through a linear transformation of the variables. The reliability of the new map is validated through nonlinear dynamic analysis. The results demonstrate that the map exhibits complex nonlinear dynamics under different parameter settings. This finding is beneficial for the construction of memristor maps and the development of image encryption algorithms.

关键词: memristive map, dynamic performance, adaptive regulation of energy

Abstract: The analysis of structure and dynamics in chaotic systems has long been a significant research direction in nonlinear science. Constructing a reliable chaotic system with rich dynamical characteristics is essential for secure communication applications. Existing memristor-based chaotic maps are typically obtained by incorporating discrete mathematical models of memristors into basic chaotic maps. In this study, a simple memristive nonlinear circuit is first designed, from which a memristive oscillator is derived. Subsequently, a memristive map is developed from this oscillator through a linear transformation of the variables. The reliability of the new map is validated through nonlinear dynamic analysis. The results demonstrate that the map exhibits complex nonlinear dynamics under different parameter settings. This finding is beneficial for the construction of memristor maps and the development of image encryption algorithms.

Key words: memristive map, dynamic performance, adaptive regulation of energy

中图分类号:  (Nonlinear dynamics and chaos)

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