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Analysis of a Fractal Josephson Junction with Unharmonic Current-Phase Relation

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Abstract

In this paper, a fractal Josephson junction with unharmonic current-phase relation is analytically and numerically analyzed. This system has two, four, or no equilibrium points depending on the external direct current source and unharmonic parameter. The stability analysis of the equilibrium points is carried out. The inclusion of unharmonic current-phase relation in an ideal Josephson junction leads to an increase in the hysteresis of current-voltage characteristics. While the inclusion of fractal characteristics in insulating layer of Josephson junction with harmonic current-phase relation leads to a decrease in the hysteresis of current-voltage characteristics. The inclusion of unharmonic current-phase relation on a fractal Josephson junction leads to an increase in the hysteresis of current-voltage characteristics. The dynamical behavior map of fractal Josephson junction with unharmonic current-phase relation in amplitude and frequency of modulation current plane is depicted. For a suitable choice of modulation parameters of external current source, fractal Josephson junction with unharmonic current-phase relation can exhibit excitable mode, bistable oscillatory mode, and periodic and chaotic behaviors.

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Acknowledgments

S.T.K. would like to thank Dr. Peguy Roussel Nwagoum Tuwa (University of Yaounde I, Cameroon) for interesting discussions.

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Authors and Affiliations

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

    Sifeu Takougang Kingni

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

    Gaetan Fautso Kuiate

  3. Department of Telecommunication and Network Engineering, IUT-Fotso Victor of Bandjoun, University of Dschang, P.O. Box: 134, Bandjoun, Cameroon

    Victor Kamdoum Tamba

  4. Institut de Mathématiques et de Sciences Physiques, Université d’Abomey-Calavi, BP 613, Porto Novo, Benin

    Adjimon Vincent Monwanou & Jean Bio Chabi Orou

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  1. Sifeu Takougang Kingni
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  2. Gaetan Fautso Kuiate
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Correspondence to Sifeu Takougang Kingni.

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Kingni, S.T., Kuiate, G.F., Tamba, V.K. et al. Analysis of a Fractal Josephson Junction with Unharmonic Current-Phase Relation. J Supercond Nov Magn 32, 2295–2301 (2019). https://doi.org/10.1007/s10948-018-4967-2

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  • DOI: https://doi.org/10.1007/s10948-018-4967-2

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