基于物理学的符号回归和哈尔波束方法来研究一个没有平衡的新的分数顺序3D混乱系统
Peiluan Li1,2, Rui Qiao1, Changjin Xu3
1School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, China.
Chaos (Woodbury, N.Y.)
|February 4, 2026
概括
本研究介绍了一种具有绝对值非线性的一种新的3D混乱系统,展示了强大的混乱动态和有效的图像加密功能. 分数顺序的概括和数值验证突出了其安全通信的潜力.
科学领域:
- 非线性动力学和混沌理论
- 分数微积分的计算.
- 密码学和安全通信
背景情况:
- 现有的混乱系统往往需要高维或复杂的非线性,对于分数顺序应用程序和安全性的验证有限.
- 需要新的混乱模型,这些模型是强大的,可计算的,适合安全通信等先进应用.
研究的目的:
- 提出和分析一个具有绝对值非线性的新的3D混乱系统.
- 将系统概括为小数阶域,并研究其混乱动态.
- 为图像加密应用分数顺序的混乱系统并评估其安全性.
主要方法:
- 开发一种具有绝对值非线性特征的新型3D混乱系统.
- 通过卡普托的分数导数和通过哈尔波纹方法进行数值分析,将其通用化为分数顺序.
- 物理信息符号回归的应用,用于方程重制和图像加密的密码分析.
主要成果:
- 拟议的3D混乱系统表现出强大的混乱行为,没有真正的平衡,由分叉图和利亚普诺夫指数证实.
- 分数顺序分析揭示了隐藏的混乱动态和持续的消散混乱,即使在1.以下的顺序.
- 图像加密算法表现出高安全性,有效抵御基于加密指标的统计和差异性攻击.
结论:
- 由于其复杂性和灵敏性,新型分数顺序混乱系统为安全通信和非线性信号处理提供了一个强大的平台.
- 开发的图像加密技术强大而高效,展示了拟议的混沌模型的实际可用性.
- 该研究验证了微积分计算在增强混乱系统属性和加密应用中的实用性.
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