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Chaotic and Hyperchaotic Dynamics of a Clapp Oscillator

Author

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  • Jiri Petrzela

    (Department of Radio Electronics, Faculty of Electrical Engineering and Communication, Brno University of Technology, Technicka 12, 616 00 Brno, Czech Republic)

Abstract

This paper describes recent findings achieved during a numerical investigation of the circuit known as the Clapp oscillator. By considering the generalized bipolar transistor as an active element and after applying the search-for-chaos optimization approach, parameter regions that lead to either chaotic or hyperchaotic dynamics were discovered. For starters, the two-port that represents the transistor was firstly assumed to have a polynomial-forward trans-conductance; then the shape of trans-conductance changes into the piecewise-linear characteristics. Both cases cause vector field symmetry and allow the coexistence of several different attractors. Chaotic and hyperchaotic behavior were deeply analyzed by using standard numerical tools such as Lyapunov exponents, basins of attraction, bifurcation diagrams, and solution sensitivity. The structural stability of strange attractors observed numerically was finally proved via a real practical experiment: a flow-equivalent chaotic oscillator was constructed as the lumped electronic circuit, and desired attractors were captured and provided as oscilloscope screenshots.

Suggested Citation

  • Jiri Petrzela, 2022. "Chaotic and Hyperchaotic Dynamics of a Clapp Oscillator," Mathematics, MDPI, vol. 10(11), pages 1-20, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:11:p:1868-:d:827682
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    References listed on IDEAS

    as
    1. Martín Alejandro Valencia-Ponce & Esteban Tlelo-Cuautle & Luis Gerardo de la Fraga, 2021. "Estimating the Highest Time-Step in Numerical Methods to Enhance the Optimization of Chaotic Oscillators," Mathematics, MDPI, vol. 9(16), pages 1-15, August.
    2. Kiliç, Recai & Yildirim, Fatma, 2008. "A survey of Wien bridge-based chaotic oscillators: Design and experimental issues," Chaos, Solitons & Fractals, Elsevier, vol. 38(5), pages 1394-1410.
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    Cited by:

    1. 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.
    2. Luigi Fortuna & Arturo Buscarino, 2022. "Analog Circuits," Mathematics, MDPI, vol. 10(24), pages 1-4, December.
    3. Yassine Bouteraa & Javad Mostafaee & Mourad Kchaou & Rabeh Abbassi & Houssem Jerbi & Saleh Mobayen, 2022. "A New Simple Chaotic System with One Nonlinear Term," Mathematics, MDPI, vol. 10(22), pages 1-17, November.
    4. Jiri Petrzela, 2023. "Chaotic States of Transistor-Based Tuned-Collector Oscillator," Mathematics, MDPI, vol. 11(9), pages 1-13, May.

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