2025年04月05日 星期六

广西师范大学学报（自然科学版） ›› 2025, Vol. 43 ›› Issue (2): 42-55.doi: 10.16088/j.issn.1001-6600.2024041605

• 物理与电子工程 • 上一篇    下一篇

基于可调宽度的多涡卷保守混沌系统的构建

颜闽秀*, 赵琦   

  1. 沈阳化工大学 信息工程学院, 辽宁 沈阳 110142
  • 收稿日期:2024-04-16 修回日期:2024-06-27 出版日期:2025-03-05 发布日期:2025-04-02
  • 通讯作者: 颜闽秀(1972—), 女, 福建仙游人, 沈阳化工大学副教授, 博士。 E-mail: yanminxiu@syuct.edu.cn
  • 基金资助:
    中国-北马其顿政府间科技合作项目(国科外〔2019〕22:6-8); 辽宁省教育厅基本科研项目(LJKMZ20220779); 辽宁省自然科学基金计划项目(2022-BS-211); 沈阳市科技计划项目(22-322-3-38)

Dynamic Analysis Multi-scroll Conservative Chaotic Systems Based on Controllable Width

YAN Minxiu*, ZHAO Qi   

  1. College of Information Engineering, Shenyang University of Chemical Technology, Shenyang Liaoning 110142, China
  • Received:2024-04-16 Revised:2024-06-27 Online:2025-03-05 Published:2025-04-02

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摘要： 相较于耗散多涡卷混沌系统,保守多涡卷混沌系统在图像加密和保密通信领域具有潜在的应用前景,具有重要研究意义。基于哈密顿能量守恒原理,本文构建一个四维保守混沌系统。通过引入分段函数扩展系统的平衡点,得到沿x和y方向上可调节宽度的多涡卷混沌系统。通过调整系统参数和初始值,能够生成具有不同能级和涡卷数目的多涡卷类吸引子。值得注意的是,随着涡卷数量的增加,系统的Lyapunov指数呈现逐步上升趋势。通过NIST测试,验证了系统在随机信号发生器以及图像加密等应用方面的潜在价值。实验结果显示,系统的SE值高达0.63,充分证明其在保密通信领域的实用性和重要性。

关键词: 混沌系统, Lyapunov指数, NIST测试, 随机信号发生器, 图像加密

Abstract: Compared with dissipative multi-scroll chaotic systems, conservative multi-scroll chaotic systems exhibit potential application prospects in image encryption and secure communication, rendering the research significantly meaningful. Based on the principle of Hamiltonian energy conservation, a four-dimensional conservative chaotic system is constructed in this peper. By introducing piecewise functions, the equilibrium points of the system are expanded, resulting in a multi-scroll chaotic system with adjustable widths along the x and y directions. By adjusting the system parameters and initial values, multi-scroll-like attractors with different energy levels and scroll numbers are generated. Notably, as the number of scrolls increases, the Lyapunov exponent of the system also exhibits a gradually increasing trend. Through NIST testing, the potential value of the system in applications such as random signal generators and image encryption is verified. Experimental results show that the SE value of the system reaches 0.63, fully demonstrating its practicality and importance in the field of secure communication.

Key words: chaotic system, Lyapunov exponent, NIST test, random signal generator, image encryption

中图分类号:  O415.5

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