IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v138y2020ics0960077920302630.html
   My bibliography  Save this article

Theoretical design and circuit implementation of novel digital chaotic systems via hybrid control

Author

Listed:
  • Zheng, Jun
  • Hu, Hanping
  • Ming, Hao
  • Liu, Xiaohui

Abstract

Chaos is a paradigm shift of all science, which provides a collection of concepts and methods to analyze a novel behavior that can arise in a wide range of disciplines. However, most of researches in simulations and applications of chaos are performed on finite-state automata, which inevitably causes chaos to collapse. Here we present a hybrid model by controlling digital system with continuous chaotic system to construct chaos on finite-state automata. A new concept and method named Generalized Symbolic Dynamics (GSD) is proposed to target the hybrid system. Based on GSD, a rigorous proof is given that the controlled digital system is chaotic in the sense of Devaney. Moreover, analog-digital hybrid circuit is built for the digital chaotic system. Finally, a simple pseudorandom number generator is designed as a proof of concept. Results show that the proposed generator has good performance for cryptography. Such digital chaotic systems, which are not subject to degradation, could pave the way for widespread applications of chaos.

Suggested Citation

  • Zheng, Jun & Hu, Hanping & Ming, Hao & Liu, Xiaohui, 2020. "Theoretical design and circuit implementation of novel digital chaotic systems via hybrid control," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
  • Handle: RePEc:eee:chsofr:v:138:y:2020:i:c:s0960077920302630
    DOI: 10.1016/j.chaos.2020.109863
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077920302630
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.chaos.2020.109863?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. Persohn, K.J. & Povinelli, R.J., 2012. "Analyzing logistic map pseudorandom number generators for periodicity induced by finite precision floating-point representation," Chaos, Solitons & Fractals, Elsevier, vol. 45(3), pages 238-245.
    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.
    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. 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).
    2. Wafaa S. Sayed & Ahmed G. Radwan & Ahmed A. Rezk & Hossam A. H. Fahmy, 2017. "Finite Precision Logistic Map between Computational Efficiency and Accuracy with Encryption Applications," Complexity, Hindawi, vol. 2017, pages 1-21, February.
    3. Chunlei Fan & Qun Ding, 2019. "Effects of Limited Computational Precision on the Discrete Chaotic Sequences and the Design of Related Solutions," Complexity, Hindawi, vol. 2019, pages 1-10, January.
    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. De Micco, L. & Antonelli, M. & Larrondo, H.A., 2017. "Stochastic degradation of the fixed-point version of 2D-chaotic maps," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 477-484.
    6. 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).
    7. Eduarda T. C. Chagas & Marcelo Queiroz‐Oliveira & Osvaldo A. Rosso & Heitor S. Ramos & Cristopher G. S. Freitas & Alejandro C. Frery, 2022. "White Noise Test from Ordinal Patterns in the Entropy–Complexity Plane," International Statistical Review, International Statistical Institute, vol. 90(2), pages 374-396, August.

    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:138:y:2020:i:c:s0960077920302630. 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.