中国物理B ›› 2026, Vol. 35 ›› Issue (7): 70504-070504.doi: 10.1088/1674-1056/ae181e

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A modular-bias-sin chaotification method for enhanced discrete memristor chaotic maps

Shu Yi(易澍)1, Huihai Wang(王会海)2,†, and Kehui Sun(孙克辉)3   

  1. 1 School of Microelectronics, Tianjin University, Tianjin 300354, China;
    2 School of Electronics Information, Central South University, Changsha 410083, China;
    3 School of Physics, Central South University, Changsha 410083, China
  • 收稿日期:2025-09-10 修回日期:2025-10-21 接受日期:2025-10-28 发布日期:2026-07-15
  • 通讯作者: Huihai Wang E-mail:wanghuihai_csu@csu.edu.cn
  • 基金资助:
    This work was supported by the National Natural Science Foundation of China (Grant Nos. 62071496 and 62061008).

A modular-bias-sin chaotification method for enhanced discrete memristor chaotic maps

Shu Yi(易澍)1, Huihai Wang(王会海)2,†, and Kehui Sun(孙克辉)3   

  1. 1 School of Microelectronics, Tianjin University, Tianjin 300354, China;
    2 School of Electronics Information, Central South University, Changsha 410083, China;
    3 School of Physics, Central South University, Changsha 410083, China
  • Received:2025-09-10 Revised:2025-10-21 Accepted:2025-10-28 Published:2026-07-15
  • Contact: Huihai Wang E-mail:wanghuihai_csu@csu.edu.cn
  • Supported by:
    This work was supported by the National Natural Science Foundation of China (Grant Nos. 62071496 and 62061008).

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摘要： This paper proposes a novel modular-bias-sin chaotification method (MBSC) to address the limitations of existing discrete memristor (DM)-based chaotic maps. By applying MBSC to several fundamental discrete memristors, the enhanced chaotic variants are constructed. Comprehensive dynamical analyses, including attractor phase diagrams, Lyapunov exponents, bifurcation diagrams, Shannon entropy (SE) complexity, and chaotic region scale (CRS), demonstrate that the MBSC-enhanced maps outperform the original DM maps and existing modified models. Specifically, they exhibit wider chaotic parameter ranges, larger Lyapunov exponents, higher SE complexity, and robust hyperchaotic behavior. To validate practical applicability, a pseudo-random number generator (PRNG) based on the enhanced chaotic maps is implemented, which passes all NIST SP 800-22 statistical tests, confirming its high randomness and suitability for security-sensitive applications.

关键词: discrete memristor, chaotification method, dynamical analyses, pseudo-random number generator

Abstract: This paper proposes a novel modular-bias-sin chaotification method (MBSC) to address the limitations of existing discrete memristor (DM)-based chaotic maps. By applying MBSC to several fundamental discrete memristors, the enhanced chaotic variants are constructed. Comprehensive dynamical analyses, including attractor phase diagrams, Lyapunov exponents, bifurcation diagrams, Shannon entropy (SE) complexity, and chaotic region scale (CRS), demonstrate that the MBSC-enhanced maps outperform the original DM maps and existing modified models. Specifically, they exhibit wider chaotic parameter ranges, larger Lyapunov exponents, higher SE complexity, and robust hyperchaotic behavior. To validate practical applicability, a pseudo-random number generator (PRNG) based on the enhanced chaotic maps is implemented, which passes all NIST SP 800-22 statistical tests, confirming its high randomness and suitability for security-sensitive applications.

Key words: discrete memristor, chaotification method, dynamical analyses, pseudo-random number generator

中图分类号:  (Nonlinear dynamics and chaos)

  • 05.45.-a
84.30.-r (Electronic circuits) 05.45.Pq (Numerical simulations of chaotic systems)