IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v611y2023ics0378437123000158.html
   My bibliography  Save this article

Fractal resistive–capacitive–inductive shunted Josephson junction: Theoretical investigation and microcontroller implementation

Author

Listed:
  • Ramadoss, Janarthanan
  • Ngongiah, Isidore Komofor
  • Chamgoué, André Chéagé
  • Kingni, Sifeu Takougang
  • Rajagopal, Karthikeyan

Abstract

The paper captures the analytical and numerical investigations of the fractal resistive–capacitive–inductive shunted Josephson junction (FRCLSJJ) and its microcontroller implementation (MCI). The rate equations of FRCLSJJ are established and based on the Routh–Hurwitz criterion, two equilibrium points are reported with one unconditionally stable and the other unstable for the direct current used for junction excitation less than or equal to one. When this current is greater than one, the FRCLSJJ exhibits no equilibrium point. The contribution of fractal parameters to the dynamics of FRCLSJJ is investigated on fast bursting, regular spiking, relaxation behaviors, and periodic bursting. The FRCLSJJ is characterized by fine dynamics such as different presentations of complex behaviors, the coexistence of periodic and chaotic hidden attractors, chaotic hidden attractors, antimonotonicity, periodic attractors, and periodic and chaotic bubble hidden attractors for varying system parameters. And in the last section of the investigation, the MCI of FRCSJJ is realized with the results establishing a qualitative agreement with numerically simulated results.

Suggested Citation

  • Ramadoss, Janarthanan & Ngongiah, Isidore Komofor & Chamgoué, André Chéagé & Kingni, Sifeu Takougang & Rajagopal, Karthikeyan, 2023. "Fractal resistive–capacitive–inductive shunted Josephson junction: Theoretical investigation and microcontroller implementation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 611(C).
    • Handle: RePEc:eee:phsmap:v:611:y:2023:i:c:s0378437123000158
    DOI: 10.1016/j.physa.2023.128460
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437123000158
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2023.128460?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Sifeu Takougang Kingni & Karthikeyan Rajagopal & Serdar Çiçek & Andre Cheukem & Victor Kamdoum Tamba & Gaetan Fautso Kuiate, 2020. "Dynamical analysis, FPGA implementation and its application to chaos based random number generator of a fractal Josephson junction with unharmonic current-phase relation," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 93(3), pages 1-11, March.
    2. Sifeu Takougang Kingni & Karthikeyan Rajagopal & Victor Kamdoum Tamba & Cyrille Ainamon & Jean Bio Chabi Orou, 2019. "Analysis and FPGA implementation of an autonomous Josephson junction snap oscillator," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 92(10), pages 1-8, October.
    3. E. Neumann & A. Pikovsky, 2003. "Slow-fast dynamics in Josephson junctions," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 34(3), pages 293-303, August.
    4. Ngongiah, Isidore Komofor & Ramakrishnan, Balamurali & Njitacke, Zeric Tabekoueng & Kuiate, Gaetan Fautso & Kingni, Sifeu Takougang, 2022. "Resistive–capacitive shunted Josephson junction with unharmonic current-phase relation: Analysis and microcontroller implementation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 603(C).
    5. Colince Welba & Dhanagopal Ramachandran & Alexendre Noura & Victor Kamdoum Tamba & Sifeu Takougang Kingni & Pascal Eloundou Ntsama & Pierre Ele & Akif Akgul, 2022. "Josephson Junction Model: FPGA Implementation and Chaos-Based Encryption of sEMG Signal through Image Encryption Technique," Complexity, Hindawi, vol. 2022, pages 1-14, February.
    6. Yang, Xiao-Song & Li, Qingdu, 2006. "A computer-assisted proof of chaos in Josephson junctions," Chaos, Solitons & Fractals, Elsevier, vol. 27(1), pages 25-30.
    7. Sifeu Takougang Kingni & Gaetan Fautso Kuiate & Romanic Kengne & Robert Tchitnga & Paul Woafo, 2017. "Analysis of a No Equilibrium Linear Resistive-Capacitive-Inductance Shunted Junction Model, Dynamics, Synchronization, and Application to Digital Cryptography in Its Fractional-Order Form," Complexity, Hindawi, vol. 2017, pages 1-12, October.
    8. John Clarke & Frank K. Wilhelm, 2008. "Superconducting quantum bits," Nature, Nature, vol. 453(7198), pages 1031-1042, June.
    9. Isidore Komofor Ngongiah & Balamurali Ramakrishnan & Hayder Natiq & Justin Roger Mboupda Pone & Gaetan Fautso Kuiate, 2022. "Josephson junction based on high critical-temperature superconductors: analysis, microcontroller implementation, and suppression of coexisting and chaotic attractors," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 95(9), pages 1-13, September.
    10. Sifeu Takougang Kingni & André Cheukem & André Cheage Chamgoué & Fulbert Togue Kamga, 2020. "Analysis of Josephson junction with topologically nontrivial barrier," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 93(8), pages 1-5, August.
    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. Isidore Komofor Ngongiah & Balamurali Ramakrishnan & Hayder Natiq & Justin Roger Mboupda Pone & Gaetan Fautso Kuiate, 2022. "Josephson junction based on high critical-temperature superconductors: analysis, microcontroller implementation, and suppression of coexisting and chaotic attractors," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 95(9), pages 1-13, September.
    2. Karthikeyan Rajagopal & Suresh Kumarasamy & Sathiyadevi Kanagaraj & Anitha Karthikeyan, 2022. "Infinitely coexisting chaotic and nonchaotic attractors in a RLC shunted Josephson Junction with an AC bias current," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 95(9), pages 1-9, September.
    3. Ngongiah, Isidore Komofor & Ramakrishnan, Balamurali & Njitacke, Zeric Tabekoueng & Kuiate, Gaetan Fautso & Kingni, Sifeu Takougang, 2022. "Resistive–capacitive shunted Josephson junction with unharmonic current-phase relation: Analysis and microcontroller implementation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 603(C).
    4. Sitan Chen & Jordan Cotler & Hsin-Yuan Huang & Jerry Li, 2023. "The complexity of NISQ," Nature Communications, Nature, vol. 14(1), pages 1-6, December.
    5. Ren, Hai-Peng & Tian, Kun & Grebogi, Celso, 2020. "Topological horseshoe in a single-scroll Chen system with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    6. Rishabh Upadhyay & Dmitry S. Golubev & Yu-Cheng Chang & George Thomas & Andrew Guthrie & Joonas T. Peltonen & Jukka P. Pekola, 2024. "Microwave quantum diode," Nature Communications, Nature, vol. 15(1), pages 1-9, December.
    7. Uçar, Ahmet & Lonngren, Karl E. & Bai, Er-Wei, 2007. "Chaos synchronization in RCL-shunted Josephson junction via active control," Chaos, Solitons & Fractals, Elsevier, vol. 31(1), pages 105-111.
    8. Ramamoorthy, Ramesh & Rajagopal, Karthikeyan & Leutcho, Gervais Dolvis & Krejcar, Ondrej & Namazi, Hamidreza & Hussain, Iqtadar, 2022. "Multistable dynamics and control of a new 4D memristive chaotic Sprott B system," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    9. Sifeu Takougang Kingni & Gaetan Fautso Kuiate & Romanic Kengne & Robert Tchitnga & Paul Woafo, 2017. "Analysis of a No Equilibrium Linear Resistive-Capacitive-Inductance Shunted Junction Model, Dynamics, Synchronization, and Application to Digital Cryptography in Its Fractional-Order Form," Complexity, Hindawi, vol. 2017, pages 1-12, October.
    10. Li, Wenlin & Li, Chong & Song, Heshan, 2016. "Realization of quantum information processing in quantum star network constituted by superconducting hybrid systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 463(C), pages 427-436.
    11. Yalçin, Müştak E., 2007. "Multi-scroll and hypercube attractors from a general jerk circuit using Josephson junctions," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1659-1666.
    12. Mezatio, Brice Anicet & Motchongom, Marceline Tingue & Wafo Tekam, Blaise Raoul & Kengne, Romanic & Tchitnga, Robert & Fomethe, Anaclet, 2019. "A novel memristive 6D hyperchaotic autonomous system with hidden extreme multistability," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 100-115.
    13. Abdel-Khalek, S. & Berrada, K. & Aldaghfag, Shatha A., 2021. "Quantum correlations and non-classical properties for two superconducting qubits interacting with a quantized field in the context of deformed Heisenberg algebra," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    14. Venditti, Claudia & Adrover, Alessandra & Giona, Massimiliano, 2022. "Inertial effects and long-term transport properties of particle motion in washboard potential," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 585(C).

    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:eee:phsmap:v:611:y:2023:i:c:s0378437123000158. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.