IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i22p4229-d970697.html
   My bibliography  Save this article

Quality Evaluation for Reconstructing Chaotic Attractors

Author

Listed:
  • Madalin Frunzete

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

Abstract

Dynamical systems are used in various applications, and their simulation is related with the type of mathematical operations used in their construction. The quality of the system is evaluated in terms of reconstructing the system, starting from its final point to the beginning (initial conditions). Deciphering a message has to be without loss, and this paper will serve to choose the proper dynamical system to be used in chaos-based cryptography. The characterization of the chaotic attractors is the most important information in order to obtain the desired behavior. Here, observability and singularity are the main notions to be used for introducing an original term: quality observability index (q.o.i.). This is an original contribution for measuring the quality of the chaotic attractors. In this paper, the q.o.i. is defined and computed in order to confirm its usability.

Suggested Citation

  • Madalin Frunzete, 2022. "Quality Evaluation for Reconstructing Chaotic Attractors," Mathematics, MDPI, vol. 10(22), pages 1-11, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:22:p:4229-:d:970697
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/22/4229/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/22/4229/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Anastasia Sofroniou & Steven Bishop, 2014. "Dynamics of a Parametrically Excited System with Two Forcing Terms," Mathematics, MDPI, vol. 2(3), pages 1-24, September.
    2. 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.
    3. Alves, P.R.L. & Duarte, L.G.S. & da Mota, L.A.C.P., 2017. "A new characterization of chaos from a time series," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 323-326.
    4. Bei Chen & Xinxin Cheng & Han Bao & Mo Chen & Quan Xu, 2022. "Extreme Multistability and Its Incremental Integral Reconstruction in a Non-Autonomous Memcapacitive Oscillator," Mathematics, MDPI, vol. 10(5), pages 1-13, February.
    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. 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.

    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. Alves, P.R.L., 2020. "Dynamic characteristic of Bitcoin cryptocurrency in the reconstruction scheme," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    2. 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.
    3. Lavinia Bîrdac & Eva Kaslik & Raluca Mureşan, 2022. "Dynamics of a Reduced System Connected to the Investigation of an Infinite Network of Identical Theta Neurons," Mathematics, MDPI, vol. 10(18), pages 1-17, September.
    4. Alves, P.R.L., 2022. "Quantifying chaos in stock markets before and during COVID-19 pandemic from the phase space reconstruction," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 202(C), pages 480-499.
    5. Alves, P.R.L. & Duarte, L.G.S. & da Mota, L.A.C.P., 2018. "Detecting chaos and predicting in Dow Jones Index," Chaos, Solitons & Fractals, Elsevier, vol. 110(C), pages 232-238.
    6. Andrei Victor Oancea & Ilie Bodale, 2022. "Chaos Synchronization of Two Györgyi–Field Systems for the Belousov–Zhabotinsky Chemical Reaction," Mathematics, MDPI, vol. 10(21), pages 1-14, October.
    7. Daniel A. Magallón & Rider Jaimes-Reátegui & Juan H. García-López & Guillermo Huerta-Cuellar & Didier López-Mancilla & Alexander N. Pisarchik, 2022. "Control of Multistability in an Erbium-Doped Fiber Laser by an Artificial Neural Network: A Numerical Approach," Mathematics, MDPI, vol. 10(17), pages 1-20, 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:10:y:2022:i:22:p:4229-:d:970697. 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.