中国物理B ›› 2025, Vol. 34 ›› Issue (8): 80502-080502.doi: 10.1088/1674-1056/add249

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Generation of multitype, multicavity chaotic attractors via impulse-function-based state variable extension

Xiaoyu Hu(胡晓宇)1,2, Siteng Wang(王思腾)1, Panpan Wu(邬盼盼)1, Hongbo Cao(曹红博)3,†, Tianwei Yang(杨天纬)1, and Zhongshuo Dong(董忠硕)1   

  1. 1 School of Electronics and Information, Northwestern Polytechnical University, Xi'an 710129, China;
    2 Shenzhen Research Institute of Northwestern Polytechnical University, Shenzhen 518057, China;
    3 School of Automation and Information Engineering, Xi'an University of Technology, Xi'an 710048, China
  • 收稿日期:2025-03-15 修回日期:2025-04-24 接受日期:2025-04-30 出版日期:2025-07-17 发布日期:2025-08-18
  • 通讯作者: Hongbo Cao E-mail:caohongbo@xaut.edu.cn
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No. 62001391), the Guangdong Basic and Applied Basic Research Foundation (Grant No. 2024A1515010308), the Natural Science Basic Research Program of Shaanxi (Grant No. 2024JC-YBQN-0464), and the Scientific Research Program Funded by Education Department of Shaanxi Provincial Government (Grant No. 24JK0559).

Generation of multitype, multicavity chaotic attractors via impulse-function-based state variable extension

Xiaoyu Hu(胡晓宇)1,2, Siteng Wang(王思腾)1, Panpan Wu(邬盼盼)1, Hongbo Cao(曹红博)3,†, Tianwei Yang(杨天纬)1, and Zhongshuo Dong(董忠硕)1   

  1. 1 School of Electronics and Information, Northwestern Polytechnical University, Xi'an 710129, China;
    2 Shenzhen Research Institute of Northwestern Polytechnical University, Shenzhen 518057, China;
    3 School of Automation and Information Engineering, Xi'an University of Technology, Xi'an 710048, China
  • Received:2025-03-15 Revised:2025-04-24 Accepted:2025-04-30 Online:2025-07-17 Published:2025-08-18
  • Contact: Hongbo Cao E-mail:caohongbo@xaut.edu.cn
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No. 62001391), the Guangdong Basic and Applied Basic Research Foundation (Grant No. 2024A1515010308), the Natural Science Basic Research Program of Shaanxi (Grant No. 2024JC-YBQN-0464), and the Scientific Research Program Funded by Education Department of Shaanxi Provincial Government (Grant No. 24JK0559).

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摘要： This paper proposes a universal impulse-function-based method for extending discrete chaotic maps, enabling flexible construction of multicavity chaotic attractors. The proposed method achieves one-directional (1D) /two-directional (2D) extensions without introducing additional nonlinear terms or altering system stability. Theoretically, the cavity quantity in arbitrary directions is controlled by adjusting impulse levels $N$, while the amplitude regulation is implemented through modifications to the proportionality parameter $\rho$. Theoretical analyses, including Lyapunov exponents (LEs) and bifurcation diagrams, are conducted, confirming that the extended maps retain the intrinsic dynamics of five rational map classes. The field-programmable gate array (FPGA) implementation results are consistent with the numerical simulation results, verifying the correctness of the theoretical analysis. The method enables the expansion of unipolar attractors and enhances entropy metrics, offering a robust framework for applications in secure communication, encryption, and chaos-based technologies.

关键词: discrete chaotic maps, impulse-function-based extension method, discrete multicavity attractors, FPGA implementation

Abstract: This paper proposes a universal impulse-function-based method for extending discrete chaotic maps, enabling flexible construction of multicavity chaotic attractors. The proposed method achieves one-directional (1D) /two-directional (2D) extensions without introducing additional nonlinear terms or altering system stability. Theoretically, the cavity quantity in arbitrary directions is controlled by adjusting impulse levels $N$, while the amplitude regulation is implemented through modifications to the proportionality parameter $\rho$. Theoretical analyses, including Lyapunov exponents (LEs) and bifurcation diagrams, are conducted, confirming that the extended maps retain the intrinsic dynamics of five rational map classes. The field-programmable gate array (FPGA) implementation results are consistent with the numerical simulation results, verifying the correctness of the theoretical analysis. The method enables the expansion of unipolar attractors and enhances entropy metrics, offering a robust framework for applications in secure communication, encryption, and chaos-based technologies.

Key words: discrete chaotic maps, impulse-function-based extension method, discrete multicavity attractors, FPGA implementation

中图分类号:  (Nonlinear dynamics and chaos)

  • 05.45.-a
05.45.Pq (Numerical simulations of chaotic systems) 05.45.Gg (Control of chaos, applications of chaos) 95.10.Fh (Chaotic dynamics)