IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v38y2008i2p439-446.html
   My bibliography  Save this article

A method of improving the properties of digital chaotic system

Author

Listed:
  • Hu, Hanping
  • Xu, Ya
  • Zhu, Ziqi

Abstract

To weaken the degradation phenomenon of digital chaotic systems with finite computing precision, the paper brings forward a varying parameter compensation method (VPCM) on the basis of the Lyapunov number. According to the differential mean-value theorem, the proposed method employs the varying parameter and Lyapunov number to improve the properties of digital chaotic systems with finite computing precision. Results of the experiments demonstrate that: the method prolongs the cycle length greatly, the digital chaotic systems achieve ergodicity in finite precision, and the distribution of digital chaotic sequences (DCSs) approximates that of real chaotic sequences (RCSs). This method can be applied to the fields of chaotic cryptography and broad spectrum communications.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:38:y:2008:i:2:p:439-446
    DOI: 10.1016/j.chaos.2006.11.027
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077906010812
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2006.11.027?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. Chee, Chin Yi & Xu, Daolin, 2005. "Secure digital communication using controlled projective synchronisation of chaos," Chaos, Solitons & Fractals, Elsevier, vol. 23(3), pages 1063-1070.
    2. Chien, Tsun-I & Liao, Teh-Lu, 2005. "Design of secure digital communication systems using chaotic modulation, cryptography and chaotic synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 24(1), pages 241-255.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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).
    3. 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).
    4. 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).

    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. Banerjee, Santo, 2009. "Synchronization of time-delayed systems with chaotic modulation and cryptography," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 745-750.
    2. Sun, Yeong-Jeu, 2009. "An exponential observer for the generalized Rossler chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2457-2461.
    3. Wafaa S. Sayed & Moheb M. R. Henein & Salwa K. Abd-El-Hafiz & Ahmed G. Radwan, 2017. "Generalized Dynamic Switched Synchronization between Combinations of Fractional-Order Chaotic Systems," Complexity, Hindawi, vol. 2017, pages 1-17, February.
    4. Shang, Li-Jen & Shyu, Kuo-Kai, 2009. "A method for extracting chaotic signal from noisy environment," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1120-1125.
    5. Gao, Tiegang & Chen, Zengqiang, 2008. "Image encryption based on a new total shuffling algorithm," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 213-220.
    6. Zaher, Ashraf A., 2009. "An improved chaos-based secure communication technique using a novel encryption function with an embedded cipher key," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2804-2814.
    7. Chien, Tsun-I & Hung, Yung-Ching & Liao, Teh-Lu, 2006. "A non-correlator-based digital communication system using interleaved chaotic differential peaks keying (I-CDPK) modulation and chaotic synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 29(4), pages 965-977.
    8. Eisencraft, Marcio & Baccalá, Luiz Antonio, 2008. "The Cramer-Rao bound for initial conditions estimation of chaotic orbits," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 132-139.
    9. Sun, Yeong-Jeu, 2009. "A simple observer of the generalized Chen chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1641-1644.
    10. Sharma, Vivek & Sharma, B.B. & Nath, R., 2017. "Nonlinear unknown input sliding mode observer based chaotic system synchronization and message recovery scheme with uncertainty," Chaos, Solitons & Fractals, Elsevier, vol. 96(C), pages 51-58.
    11. Peng, Qiu & Jian, Jigui, 2021. "Estimating the ultimate bounds and synchronization of fractional-order plasma chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    12. Vasegh, Nastaran & Khellat, F., 2009. "Projective synchronization of chaotic time-delayed systems via sliding mode controller," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1054-1061.
    13. Ge, Zheng-Ming & Lin, Guo-Hua, 2007. "The complete, lag and anticipated synchronization of a BLDCM chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 34(3), pages 740-764.
    14. Sun, Yeong-Jeu, 2009. "Robust tracking control of uncertain Duffing–Holmes control systems," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1282-1287.
    15. Wen, Guilin & Xu, Daolin, 2005. "Nonlinear observer control for full-state projective synchronization in chaotic continuous-time systems," Chaos, Solitons & Fractals, Elsevier, vol. 26(1), pages 71-77.
    16. Zhao, Ming-Chao & Li, Ke-Zan & Fu, Xin-Chu, 2009. "Modified one-way coupled map lattices as communication cryptosystems," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 286-290.
    17. Zhang, Weiwei & Sha, Chunlin & Cao, Jinde & Wang, Guanglan & Wang, Yuan, 2021. "Adaptive quaternion projective synchronization of fractional order delayed neural networks in quaternion field," Applied Mathematics and Computation, Elsevier, vol. 400(C).
    18. Sun, Yeong-Jeu, 2009. "Solution bounds of generalized Lorenz chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 691-696.
    19. Jiri Petrzela, 2022. "Chaos in Analog Electronic Circuits: Comprehensive Review, Solved Problems, Open Topics and Small Example," Mathematics, MDPI, vol. 10(21), pages 1-28, November.
    20. Gao, Haojiang & Zhang, Yisheng & Liang, Shuyun & Li, Dequn, 2006. "A new chaotic algorithm for image encryption," Chaos, Solitons & Fractals, Elsevier, vol. 29(2), pages 393-399.

    More about this item

    Statistics

    Access and download statistics

    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:38:y:2008:i:2:p:439-446. 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.