IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v104y2017icp477-484.html
   My bibliography  Save this article

Stochastic degradation of the fixed-point version of 2D-chaotic maps

Author

Listed:
  • De Micco, L.
  • Antonelli, M.
  • Larrondo, H.A.

Abstract

This paper deals with a family of interesting 2D-quadratic maps proposed by Sprott, in his seminal paper [1], related to “chaotic art”. Our main interest about these maps is their great potential for using them in digital electronic applications because they present multiple chaotic attractors depending on the selected point in the parameter’s space. Only results for the analytical representation of these maps have been published in the open literature. Consequently, the objective of this paper is to extend the analysis to the digital version, to make possible the hardware implementation in a digital medium, like field programmable gate arrays (FPGA) in fixed-point arithmetic. Our main contributions are: (a) the study of the domains of attraction in fixed-point arithmetic, in terms of period lengths and statistical properties; (b) the determination of the threshold of the bus width that preserves the integrity of the domain of attraction and (c) the comparison between two quantifiers based on respective probability distribution functions (PDFs) and the well known maximum Lyapunov exponent (MLE) to detect the above mentioned threshold.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:104:y:2017:i:c:p:477-484
    DOI: 10.1016/j.chaos.2017.09.007
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077917303776
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2017.09.007?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. Liao, Shijun, 2013. "On the numerical simulation of propagation of micro-level inherent uncertainty for chaotic dynamic systems," Chaos, Solitons & Fractals, Elsevier, vol. 47(C), pages 1-12.
    3. De Micco, Luciana & Fernández, Juana Graciela & Larrondo, Hilda A. & Plastino, Angelo & Rosso, Osvaldo A., 2012. "Sampling period, statistical complexity, and chaotic attractors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(8), pages 2564-2575.
    4. Nepomuceno, Erivelton Geraldo & Mendes, Eduardo M.A.M., 2017. "On the analysis of pseudo-orbits of continuous chaotic nonlinear systems simulated using discretization schemes in a digital computer," Chaos, Solitons & Fractals, Elsevier, vol. 95(C), pages 21-32.
    5. Smaoui, Nejib & Kanso, Ali, 2009. "Cryptography with chaos and shadowing," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2312-2321.
    6. De Micco, L. & González, C.M. & Larrondo, H.A. & Martin, M.T. & Plastino, A. & Rosso, O.A., 2008. "Randomizing nonlinear maps via symbolic dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(14), pages 3373-3383.
    7. Martin, M.T. & Plastino, A. & Rosso, O.A., 2006. "Generalized statistical complexity measures: Geometrical and analytical properties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 369(2), pages 439-462.
    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. 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.
    2. Bariviera, Aurelio F. & Font-Ferrer, Alejandro & Sorrosal-Forradellas, M. Teresa & Rosso, Osvaldo A., 2019. "An information theory perspective on the informational efficiency of gold price," The North American Journal of Economics and Finance, Elsevier, vol. 50(C).
    3. Aurelio F. Bariviera & Luciano Zunino & Osvaldo A. Rosso, 2016. "Crude Oil Market And Geopolitical Events: An Analysis Based On Information-Theory-Based Quantifiers," Fuzzy Economic Review, International Association for Fuzzy-set Management and Economy (SIGEF), vol. 21(1), pages 41-51, May.
    4. Rosso, Osvaldo A. & Carpi, Laura C. & Saco, Patricia M. & Gómez Ravetti, Martín & Plastino, Angelo & Larrondo, Hilda A., 2012. "Causality and the entropy–complexity plane: Robustness and missing ordinal patterns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(1), pages 42-55.
    5. 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).
    6. Argyroudis, George S. & Siokis, Fotios M., 2019. "Spillover effects of Great Recession on Hong-Kong’s Real Estate Market: An analysis based on Causality Plane and Tsallis Curves of Complexity–Entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 576-586.
    7. De Micco, Luciana & Fernández, Juana Graciela & Larrondo, Hilda A. & Plastino, Angelo & Rosso, Osvaldo A., 2012. "Sampling period, statistical complexity, and chaotic attractors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(8), pages 2564-2575.
    8. Aurelio F. Bariviera & Luciano Zunino & M. Belen Guercio & Lisana B. Martinez & Osvaldo A. Rosso, 2015. "Efficiency and credit ratings: a permutation-information-theory analysis," Papers 1509.01839, arXiv.org.
    9. Aquino, Andre L.L. & Ramos, Heitor S. & Frery, Alejandro C. & Viana, Leonardo P. & Cavalcante, Tamer S.G. & Rosso, Osvaldo A., 2017. "Characterization of electric load with Information Theory quantifiers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 465(C), pages 277-284.
    10. Kowalski, A.M. & Martín, M.T. & Plastino, A. & Rosso, O.A., 2011. "Fisher information description of the classical–quantal transition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(12), pages 2435-2441.
    11. Zhang, Xiaofang & Li, Hongqing & Jiang, Wenan & Chen, Liqun & Bi, Qinsheng, 2022. "Exploiting multiple-frequency bursting of a shape memory oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    12. Fernandes, Leonardo H.S. & de Araujo, Fernando H.A. & Tabak, Benjamin M., 2021. "Insights from the (in)efficiency of Chinese sectoral indices during COVID-19," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 578(C).
    13. Nepomuceno, Erivelton Geraldo & Mendes, Eduardo M.A.M., 2017. "On the analysis of pseudo-orbits of continuous chaotic nonlinear systems simulated using discretization schemes in a digital computer," Chaos, Solitons & Fractals, Elsevier, vol. 95(C), pages 21-32.
    14. Mastroeni, Loretta & Mazzoccoli, Alessandro & Vellucci, Pierluigi, 2024. "Wavelet entropy and complexity–entropy curves approach for energy commodity price predictability amid the transition to alternative energy sources," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    15. Montani, Fernando & Deleglise, Emilia B. & Rosso, Osvaldo A., 2014. "Efficiency characterization of a large neuronal network: A causal information approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 401(C), pages 58-70.
    16. F. J. Alonso & M. C. Bueso & J. M. Angulo, 2016. "Dependence Assessment Based on Generalized Relative Complexity: Application to Sampling Network Design," Methodology and Computing in Applied Probability, Springer, vol. 18(3), pages 921-933, September.
    17. Katchanov, Yurij L. & Markova, Yulia V., 2022. "Dynamics of senses of new physics discourse: Co-keywords analysis," Journal of Informetrics, Elsevier, vol. 16(1).
    18. Calbet, Xavier & López-Ruiz, Ricardo, 2007. "Extremum complexity distribution of a monodimensional ideal gas out of equilibrium," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(2), pages 523-530.
    19. Fernandes, Leonardo H.S. & de Araújo, Fernando H.A. & Silva, Igor E.M. & Neto, Jusie S.P., 2021. "Macroeconophysics indicator of economic efficiency," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 573(C).
    20. Aurelio Fernandez Bariviera & María Belén Guercio & Lisana B. Martinez & Osvaldo A. Rosso, 2015. "The (in)visible hand in the Libor market: an information theory approach," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 88(8), pages 1-9, 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:104:y:2017:i:c:p:477-484. 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.