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Dynamical analysis, FPGA implementation and its application to chaos based random number generator of a fractal Josephson junction with unharmonic current-phase relation

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Abstract

The dynamical characteristics and its applications to random number generator of a fractal Josephson junction with unharmonic current-phase relation (FJJUCPR) described by a linear resistive-capacitive-inductance shunted junction (LRCLSJ) model are investigated in this paper. The dependence of the equilibrium points of the system to the external current source or the unharmonic current-phase relation (UCPR) parameter is revealed and their stability are analysed. The inclusion of unharmonic current-phase relation in an ideal or a fractal Josephson junction leads to transform the spiking, bursting and relaxations oscillations to an excitable mode. While the inclusion of fractal characteristics in insulating layer of Josephson junction leads to an increase of the amplitude of the spiking, bursting and relaxations oscillations. The numerical simulations results also indicate that FJJUCPR exhibits self-excited chaotic attractors and two different shapes of hidden chaotic attractors. The FJJUCPR is implemented in field programmable gate arrays (FPGA) in order to validate the numerical simulations results. In addition, random number generator design is performed using chaotic signals of the FJJUCPR. The random number generator design results are successful in the NIST SP 800-22 test.

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Authors and Affiliations

  1. Department of Mechanical, Petroleum and Gas Engineering, Faculty of Mines and Petroleum Industries, University of Maroua, PO Box 46, Maroua, Cameroon

    Sifeu Takougang Kingni

  2. Center for Nonlinear Dynamics, Defence University, Bishoftu, 6020, Ethiopia

    Karthikeyan Rajagopal

  3. Institute of Energy, Mekelle University, Mekelle 121, Ethiopia

    Karthikeyan Rajagopal

  4. Department of Electronic and Automation, Vocational School of Hacibektaş, Nevşehir Hacibektaş Veli University, 50800, Hacibektaş, Nevşehir, Turkey

    Serdar Çiçek

  5. Research Unit of automation and applied computer, Electrical Engineering Department of IUT-FV, University of Dschang, PO Box 134, Bandjoun, Cameroon

    Andre Cheukem

  6. Department of Telecommunication and Network Engineering, IUT-Fotso Victor of Bandjoun, University of Dschang, PO Box 134, Bandjoun, Cameroon

    Victor Kamdoum Tamba

  7. Department of Physics, Higher Teacher Training College, University of Bamenda, PO Box 39, Bamenda, Cameroon

    Gaetan Fautso Kuiate

Authors
  1. Sifeu Takougang Kingni
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  2. Karthikeyan Rajagopal
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  3. Serdar Çiçek
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  4. Andre Cheukem
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  5. Victor Kamdoum Tamba
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  6. Gaetan Fautso Kuiate
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Correspondence to Sifeu Takougang Kingni.

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Kingni, S.T., Rajagopal, K., Çiçek, S. et al. Dynamical analysis, FPGA implementation and its application to chaos based random number generator of a fractal Josephson junction with unharmonic current-phase relation. Eur. Phys. J. B 93, 44 (2020). https://doi.org/10.1140/epjb/e2020-100562-9

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  • DOI: https://doi.org/10.1140/epjb/e2020-100562-9

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