IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v169y2023ics0960077923001595.html
   My bibliography  Save this article

Design and geometric control of polynomial chaotic maps with any desired positive Lyapunov exponents

Author

Listed:
  • Fan, Chunlei
  • Ding, Qun

Abstract

Digital chaotic maps are severely hampered by the finite calculation accuracy of the hardware device that is used to implement them, and their applications in cryptography and information assurance are seriously degraded. To resolve this issue, we put forward a universal iterative model to construct non-degenerate polynomial chaotic maps with any desired number of positive Lyapunov exponents. In addition, we innovatively propose the geometric control methods of polynomial chaotic maps, including amplitude control, offset boosting, plane rotation, shape control, and combined regulation. Furthermore, to assess the effectiveness and feasibility of the proposed method, a microcontroller-based platform was developed to demonstrate the hardware implementation and geometric control of the proposed polynomial chaotic map. Finally, a PRNG is constructed by interval quantization. Numerical experiments are performed to verify the desirable statistical properties of the PRNG in terms of local weak random test, discrete Fourier transform test, linear complexity and NIST SP800-22 test.

Suggested Citation

  • Fan, Chunlei & Ding, Qun, 2023. "Design and geometric control of polynomial chaotic maps with any desired positive Lyapunov exponents," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    • Handle: RePEc:eee:chsofr:v:169:y:2023:i:c:s0960077923001595
    DOI: 10.1016/j.chaos.2023.113258
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077923001595
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2023.113258?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Singh, Jay Prakash & Roy, Binoy Krishna & Jafari, Sajad, 2018. "New family of 4-D hyperchaotic and chaotic systems with quadric surfaces of equilibria," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 243-257.
    2. Hu, Hanping & Xu, Ya & Zhu, Ziqi, 2008. "A method of improving the properties of digital chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 38(2), pages 439-446.
    3. Zheng, Jun & Hu, Hanping, 2022. "Bit cyclic shift method to reinforce digital chaotic maps and its application in pseudorandom number generator," Applied Mathematics and Computation, Elsevier, vol. 420(C).
    4. Tutueva, Aleksandra V. & Nepomuceno, Erivelton G. & Karimov, Artur I. & Andreev, Valery S. & Butusov, Denis N., 2020. "Adaptive chaotic maps and their application to pseudo-random numbers generation," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    5. Valle, João & Machicao, Jeaneth & Bruno, Odemir M., 2022. "Chaotical PRNG based on composition of logistic and tent maps using deep-zoom," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    6. Bao, H. & Gu, Y. & Xu, Q. & Zhang, X. & Bao, B., 2022. "Parallel bi-memristor hyperchaotic map with extreme multistability," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    7. Huang, Lilian & Liu, Jin & Xiang, Jianhong & Zhang, Zefeng & Du, Xiuli, 2022. "A construction method of N-dimensional non-degenerate discrete memristive hyperchaotic map," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Fan, Chunlei & Ding, Qun, 2023. "Constructing n-dimensional discrete non-degenerate hyperchaotic maps using QR decomposition," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    2. Ostrovskii, Valerii Yu. & Rybin, Vyacheslav G. & Karimov, Artur I. & Butusov, Denis N., 2022. "Inducing multistability in discrete chaotic systems using numerical integration with variable symmetry," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    3. Wu, Zihua & Zhang, Yinxing & Bao, Han & Lan, Rushi & Hua, Zhongyun, 2024. "nD-CS: A circularly shifting chaotic map generation method," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    4. Yuan, Fang & Xing, Guibin & Deng, Yue, 2023. "Flexible cascade and parallel operations of discrete memristor," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    5. Fan, Zhenyi & Zhang, Chenkai & Wang, Yiming & Du, Baoxiang, 2023. "Construction, dynamic analysis and DSP implementation of a novel 3D discrete memristive hyperchaotic map," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    6. Zhou, Ling & You, Zhenzhen & Tang, Yun, 2021. "A new chaotic system with nested coexisting multiple attractors and riddled basins," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    7. Othman Abdullah Almatroud & Viet-Thanh Pham & Giuseppe Grassi & Mohammad Alshammari & Sahar Albosaily & Van Van Huynh, 2023. "Design of High-Dimensional Maps with Sine Terms," Mathematics, MDPI, vol. 11(17), pages 1-10, August.
    8. Zheng, Jun & Hu, Hanping & Ming, Hao & Zhang, Yanxia, 2021. "Design of a hybrid model for construction of digital chaos and local synchronization," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    9. Shihong Zhang & Hu Shi & Baizhong Wang & Chunlu Ma & Qinghua Li, 2024. "A Dynamic Hierarchical Improved Tyrannosaurus Optimization Algorithm with Hybrid Topology Structure," Mathematics, MDPI, vol. 12(10), pages 1-35, May.
    10. Yan, Yanjun & Chen, Kai & Zhao, Yijiu & Wang, Houjun & Xu, Bo & Wang, Yifan, 2024. "An innovative orthogonal matrix based on nonlinear chaotic system for compressive sensing," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    11. Dong, Youheng & Zhao, Geng, 2021. "A spatiotemporal chaotic system based on pseudo-random coupled map lattices and elementary cellular automata," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    12. García-Grimaldo, Claudio & Campos-Cantón, Eric, 2023. "Exploring a family of Bernoulli-like shift chaotic maps and its amplitude control," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    13. Zhao, Qianhan & Bao, Han & Zhang, Xi & Wu, Huagan & Bao, Bocheng, 2024. "Complexity enhancement and grid basin of attraction in a locally active memristor-based multi-cavity map," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    14. Wenqiang Yang & Li Xiao & Junjian Huang & Jinyue Yang, 2021. "Fixed-Time Synchronization of Neural Networks Based on Quantized Intermittent Control for Image Protection," Mathematics, MDPI, vol. 9(23), pages 1-14, November.
    15. Hongyan Zang & Mengdan Tai & Xinyuan Wei, 2022. "Image Encryption Schemes Based on a Class of Uniformly Distributed Chaotic Systems," Mathematics, MDPI, vol. 10(7), pages 1-21, March.
    16. Sukegawa, Noriyoshi & Ikeguchi, Tohru, 2022. "How to perturb Bernoulli shift map," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    17. Artur I. Karimov & Ekaterina Kopets & Erivelton G. Nepomuceno & Denis Butusov, 2021. "Integrate-and-Differentiate Approach to Nonlinear System Identification," Mathematics, MDPI, vol. 9(23), pages 1-19, November.
    18. Grime, Gabriel C. & Roberto, Marisa & Viana, Ricardo L. & Elskens, Yves & Caldas, Iberê L., 2023. "Biquadratic nontwist map: a model for shearless bifurcations," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    19. Nazarimehr, Fahimeh & Rajagopal, Karthikeyan & Khalaf, Abdul Jalil M. & Alsaedi, Ahmed & Pham, Viet-Thanh & Hayat, Tasawar, 2018. "Investigation of dynamical properties in a chaotic flow with one unstable equilibrium: Circuit design and entropy analysis," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 7-13.
    20. Weichao He & Yuemin Zheng & Jin Tao & Yujuan Zhou & Jiayan Wen & Qinglin Sun, 2023. "A Novel Fractional-Order Active Disturbance Rejection Load Frequency Control Based on An Improved Marine Predator Algorithm," Sustainability, MDPI, vol. 15(13), pages 1-23, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:169:y:2023:i:c:s0960077923001595. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.