李雅普诺夫指数
伪随机数发生器
随机性
参数统计
混乱的
计算机科学
混沌(操作系统)
数学
多项式的
应用数学
算法
多项式混沌
统计物理学
数学分析
人工智能
蒙特卡罗方法
物理
统计
计算机安全
作者
Zhongyun Hua,Yongyong Chen,Han Bao,Yicong Zhou
出处
期刊:IEEE transactions on systems, man, and cybernetics
[Institute of Electrical and Electronics Engineers]
日期:2022-07-01
卷期号:52 (7): 4402-4414
被引量:47
标识
DOI:10.1109/tsmc.2021.3096967
摘要
When used in engineering applications, most existing chaotic systems may have many disadvantages, including discontinuous chaotic parameter ranges, lack of robust chaos, and easy occurrence of chaos degradation. In this article, we propose a two-dimensional (2-D) parametric polynomial chaotic system (2D-PPCS) as a general system that can yield many 2-D chaotic maps with different exponent coefficient settings. The 2D-PPCS initializes two parametric polynomials and then applies modular chaotification to the polynomials. Setting different control parameters allows the 2D-PPCS to customize its Lyapunov exponents in order to obtain robust chaos and behaviors with desired complexity. Our theoretical analysis demonstrates the robust chaotic behavior of the 2D-PPCS. Two illustrative examples are provided and tested based on numeral experiments to verify the effectiveness of the 2D-PPCS. A chaos-based pseudorandom number generator is also developed to illustrate the applications of the 2D-PPCS. The experimental results demonstrate that these examples of the 2D-PPCS can achieve robust and desired chaos, have better performance, and generate higher randomness pseudorandom numbers than some representative 2-D chaotic maps.
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