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

Author

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  • 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
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    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. 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.
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    7. 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.
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