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Chaos in Analog Electronic Circuits: Comprehensive Review, Solved Problems, Open Topics and Small Example

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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 strives to achieve a comprehensive review of chaos in analog circuits and lumped electronic networks. Readers will be guided from the beginning of the investigations of simple electronic circuits to the current trends in the research into chaos. The author tries to provide the key references related to this issue, including papers describing modern numerical algorithms capable of localizing chaotic and hyperchaotic motion in complex mathematical models, interesting full on-chip implementations of chaotic systems, possible practical applications of entropic signals, fractional-order chaotic systems and chaotic oscillators with mem-elements.

Suggested Citation

  • 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.
  • Handle: RePEc:gam:jmathe:v:10:y:2022:i:21:p:4108-:d:962852
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    References listed on IDEAS

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    1. Bao, B.C. & Bao, H. & Wang, N. & Chen, M. & Xu, Q., 2017. "Hidden extreme multistability in memristive hyperchaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 94(C), pages 102-111.
    2. 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.
    3. Jiri Petrzela & Miroslav Rujzl, 2022. "Chaotic Oscillations in Cascoded and Darlington-Type Amplifier Having Generalized Transistors," Mathematics, MDPI, vol. 10(3), pages 1-25, February.
    4. Yousuf Islam & Chunbiao Li & Yicheng Jiang & Xu Ma & Akif Akgul & M. De Aguiar, 2022. "A Hidden Chaotic Attractor with an Independent Amplitude-Frequency Controller," Complexity, Hindawi, vol. 2022, pages 1-11, March.
    5. Natsheh, Ammar N. & Kettleborough, J. Gordon & Janson, Natalia B., 2009. "Experimental study of controlling chaos in a DC–DC boost converter," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2500-2508.
    6. Jiri Petrzela, 2020. "New Chaotic Oscillator Derived from Class C Single Transistor-Based Amplifier," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-18, November.
    7. Minati, L. & Gambuzza, L.V. & Thio, W.J. & Sprott, J.C. & Frasca, M., 2020. "A chaotic circuit based on a physical memristor," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    8. Li, Hong & Zhang, Bo & Li, Zhong & Halang, Wolfgang A. & Chen, Guanrong, 2009. "Controlling DC–DC converters by chaos-based pulse width modulation to reduce EMI," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1378-1387.
    9. Othman Abdullah Almatroud & Victor Kamdoum Tamba & Giuseppe Grassi & Viet-Thanh Pham, 2021. "An Oscillator without Linear Terms: Infinite Equilibria, Chaos, Realization, and Application," Mathematics, MDPI, vol. 9(24), pages 1-15, December.
    10. Njitacke, Z.T. & kengne, J. & Fotsin, H.B. & Negou, A. Nguomkam & Tchiotsop, D., 2016. "Coexistence of multiple attractors and crisis route to chaos in a novel memristive diode bidge-based Jerk circuit," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 180-197.
    11. Jiri Petrzela, 2022. "Chaotic and Hyperchaotic Dynamics of a Clapp Oscillator," Mathematics, MDPI, vol. 10(11), pages 1-20, May.
    12. Wafo Tekam, Raoul Blaise & Kengne, Jacques & Djuidje Kenmoe, Germaine, 2019. "High frequency Colpitts’ oscillator: A simple configuration for chaos generation," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 351-360.
    13. Jose-Cruz Nuñez-Perez & Vincent-Ademola Adeyemi & Yuma Sandoval-Ibarra & Francisco-Javier Perez-Pinal & Esteban Tlelo-Cuautle, 2021. "Maximizing the Chaotic Behavior of Fractional Order Chen System by Evolutionary Algorithms," Mathematics, MDPI, vol. 9(11), pages 1-22, May.
    14. Chien, Tsun-I & Liao, Teh-Lu, 2005. "Design of secure digital communication systems using chaotic modulation, cryptography and chaotic synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 24(1), pages 241-255.
    15. Chen, Liping & Pan, Wei & Wu, Ranchao & Wang, Kunpeng & He, Yigang, 2016. "Generation and circuit implementation of fractional-order multi-scroll attractors," Chaos, Solitons & Fractals, Elsevier, vol. 85(C), pages 22-31.
    16. 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.
    17. Signing, V.R. Folifack & Kengne, J. & Pone, J.R. Mboupda, 2019. "Antimonotonicity, chaos, quasi-periodicity and coexistence of hidden attractors in a new simple 4-D chaotic system with hyperbolic cosine nonlinearity," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 187-198.
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    1. Luigi Fortuna & Arturo Buscarino, 2022. "Analog Circuits," Mathematics, MDPI, vol. 10(24), pages 1-4, December.

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