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

doi:10.1088/1674-1056/add249

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.

Keywords: discrete chaotic maps impulse-function-based extension method discrete multicavity attractors FPGA implementation

Received: 15 March 2025
Revised: 24 April 2025
Accepted manuscript online: 30 April 2025

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

Fund: 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).

Corresponding Authors: Hongbo Cao
E-mail: caohongbo@xaut.edu.cn

Cite this article:

Xiaoyu Hu(胡晓宇), Siteng Wang(王思腾), Panpan Wu(邬盼盼), Hongbo Cao(曹红博), Tianwei Yang(杨天纬), and Zhongshuo Dong(董忠硕) Generation of multitype, multicavity chaotic attractors via impulse-function-based state variable extension 2025 Chin. Phys. B 34 080502

[1] Yu F, Shen H, Yu Q, Kong X, Sharma P K and Cai S 2023 IEEE Trans. Netw. Sci. Eng. 10 845
[2] Lai Q and Chen Z 2023 Chaos Solitons Fractals 170 113341
[3] Lin H, Deng X, Yu F and Sun Y 2025 IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst. 44 304
[4] Cao Y and Liu H 2025 Integr. 100 102302
[5] Lin Z and Liu H 2024 Eur. Phys. J. Spec. Top. 233 1373
[6] Xu D and Liu H 2023 Int. J. Bifurcation Chaos 33 2350177
[7] Peng H, Jié M, Du X, Duan S and Wang L 2023 Chaos Solitons Fractals 174 113803
[8] Madouri Z B, Hadj Said N and Ali Pacha A 2024 J. Opt. 53 3548
[9] Zhao W, Chang Z, Ma C and Shen Z 2023 Entropy 25 166
[10] Lai Q, Yang L and Chen G 2025 IEEE Trans. Ind. Electron. 72 969
[11] Lai Q and Yang L 2023 Chaos Solitons Fractals 174 113807
[12] Darani A Y, Yengejeh Y K, Pakmanesh H and Navarro G 2024 Chaos Solitons Fractals 179 114396
[13] Huang L and Gao H 2024 IEEE Trans. Circuits Syst. I Regul. Pap. 71 3726
[14] Moon S, Baik J J and Seo J M 2021 Commun. Nonlinear Sci. Numer. Simul. 96 105708
[15] Chen R, Zhang F, Teng L, et al. 2023 J. Opt. 52 2109
[16] Lai Q, Liu Y and Fortuna L 2024 IEEE Trans. Circuits Syst. I Regul. Pap. 71 4665
[17] Lorenz E N 1963 J. Atmos. Sci. 20 130
[18] Bao H, Rong K, Chen M, Zhang X and Bao B 2023 Chaos Solitons Fractals 174 113844
[19] Xu B, Tang Z, Ye X, et al. 2024 Nonlinear Dyn.
[20] Li K, Wang Q, Zheng Q, et al. 2025 Nonlinear Dyn. 113 861
[21] Lin H, Wang C and Sun Y 2024 IEEE Trans. Ind. Electron. 71 7806
[22] Bao H, Xi M, Wang N, et al. 2024 Nonlinear Dyn. 112 12521
[23] Xiao Y, Sun K and He S 2020 Eur. Phys. J. Plus 135 21
[24] ZhuW, Sun K, He S,Wang H and Liu W 2023 Chaos Solitons Fractals 170 113370
[25] Hong Q, Xie Q and Xiao P 2017 Nonlinear Dyn. 87 1015
[26] Hong Q, Li Y, Wang X and Zeng Z 2019 IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst. 38 1480
[27] Zhang L, Liu Y,Wei Z, Jiang H and Bi Q 2022 Chin. Phys. B 31 030503
[28] Kuznetsov Y A 2023 Elements of Applied Bifurcation Theory 4th ed Applied Mathematical Sciences (Springer Cham)

[1]	Memristor hyperchaos in a generalized Kolmogorov-type system with extreme multistability Xiaodong Jiao(焦晓东), Mingfeng Yuan(袁明峰), Jin Tao(陶金), Hao Sun(孙昊), Qinglin Sun(孙青林), and Zengqiang Chen(陈增强). Chin. Phys. B, 2023, 32(1): 010507.
[2]	Heterogeneous dual memristive circuit: Multistability, symmetry, and FPGA implementation Yi-Zi Cheng(承亦梓), Fu-Hong Min(闵富红), Zhi Rui(芮智), and Lei Zhang(张雷). Chin. Phys. B, 2021, 30(12): 120502.
[3]	Study on a new chaotic bitwise dynamical system and its FPGA implementation Wang Qian-Xue (王倩雪), Yu Si-Min (禹思敏), C. Guyeux, J. Bahi, Fang Xiao-Le (方晓乐). Chin. Phys. B, 2015, 24(6): 060503.
[4]	Design and FPGA Implementation of a new hyperchaotic system Wang Guang-Yi(王光义), Bao Xu-Lei(包旭雷), and Wang Zhong-Lin(王忠林). Chin. Phys. B, 2008, 17(10): 3596-3602.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

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

Cite this article:

Online attention