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A computer-assisted proof of chaos in Josephson junctions

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  • Yang, Xiao-Song
  • Li, Qingdu

Abstract

This paper presents a rigorous verification of chaos in the RCLSJ model for studying dynamics of the Josephson junction. By carefully picking a suitable cross-section with respect to the attractor, it is shown that for the corresponding Poincaré map P obtained in terms of second return time, there exists a closed invariant set Λ in this cross-section such that P∣Λ is semi-conjugate to a 2-shift map, thus showing existence of chaos in the RCLSJ model.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:27:y:2006:i:1:p:25-30
    DOI: 10.1016/j.chaos.2005.04.017
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    Cited by:

    1. 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).
    2. 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).
    3. 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.
    4. 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.
    5. 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.

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