IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i2p305-d1027908.html
   My bibliography  Save this article

Singularity, Observability and Statistical Independence in the Context of Chaotic Systems

Author

Listed:
  • Alexandru Dinu

    (Faculty of Electronics, Telecommunications and Information Technology, University Politehnica of Bucharest, 061071 Bucharest, Romania)

  • Madalin Frunzete

    (Faculty of Electronics, Telecommunications and Information Technology, University Politehnica of Bucharest, 061071 Bucharest, Romania)

Abstract

Pseudorandom number generators (PRNGs) have always been a central research topic in data science, and chaotic dynamical systems are one of the means to obtain scientifically proven data. Chaotic dynamical systems have the property that they have a seemingly unpredictable and random behavior obtained by making use of deterministic laws. The current paper will show how several notions used in the study of chaotic systems—statistical independence, singularity, and observability—can be used together as a suite of test methods for chaotic systems with high potential of being used in the PRNG or cryptography fields. In order to address these topics, we relied on the adaptation of the observability coefficient used in previous papers of the authors, we calculated the singularity areas for the chaotic systems considered, and we evaluated the selected chaotic maps from a statistical independence point of view. By making use of the three notions above, we managed to find strong correlations between the methods proposed, thus supporting the idea that the resulting test procedure is consistent. Future research directions consist of applying the proposed test procedure to other chaotic systems in order to gather more data and formalize the approach in a test suite that can be used by the data scientist when selecting the best chaotic system for a specific use (PRNG, cryptography, etc.).

Suggested Citation

  • Alexandru Dinu & Madalin Frunzete, 2023. "Singularity, Observability and Statistical Independence in the Context of Chaotic Systems," Mathematics, MDPI, vol. 11(2), pages 1-17, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:2:p:305-:d:1027908
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/2/305/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/2/305/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Madalin Frunzete, 2022. "Quality Evaluation for Reconstructing Chaotic Attractors," Mathematics, MDPI, vol. 10(22), pages 1-11, November.
    2. Víctor Gayoso Martínez & Luis Hernández-Álvarez & Luis Hernández Encinas, 2020. "Analysis of the Cryptographic Tools for Blockchain and Bitcoin," Mathematics, MDPI, vol. 8(1), pages 1-14, January.
    3. J. Perez-Padron & C. Posadas-Castillo & J. Paz-Perez & E. Zambrano-Serrano & M. A. Platas-Garza, 2021. "FPGA Realization and Lyapunov–Krasovskii Analysis for a Master-Slave Synchronization Scheme Involving Chaotic Systems and Time-Delay Neural Networks," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-17, September.
    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. Madalin Frunzete, 2022. "Quality Evaluation for Reconstructing Chaotic Attractors," Mathematics, MDPI, vol. 10(22), pages 1-11, November.
    2. Avinash Vijayarangan & Veena Narayanan & Vijayarangan Natarajan & Srikanth Raghavendran, 2022. "Novel Authentication Protocols Based on Quadratic Diophantine Equations," Mathematics, MDPI, vol. 10(17), pages 1-10, September.

    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:gam:jmathe:v:11:y:2023:i:2:p:305-:d:1027908. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.