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Quality Evaluation for Reconstructing Chaotic Attractors

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  • 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
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    References listed on IDEAS

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    1. 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.
    2. Anastasia Sofroniou & Steven Bishop, 2014. "Dynamics of a Parametrically Excited System with Two Forcing Terms," Mathematics, MDPI, vol. 2(3), pages 1-24, 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.
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    Citations

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    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.

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