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

  • Sifeu Takougang KingniEmail author
  • Gaetan Fautso Kuiate
  • Victor Kamdoum Tamba
  • Adjimon Vincent Monwanou
  • Jean Bio Chabi Orou
Original Paper


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.


Fractal Josephson junction Unharmonic current-phase relation Hysteresis Current-voltage characteristics Bistability Chaotic behavior 



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


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Sifeu Takougang Kingni
    • 1
    Email author
  • Gaetan Fautso Kuiate
    • 2
  • Victor Kamdoum Tamba
    • 3
  • Adjimon Vincent Monwanou
    • 4
  • Jean Bio Chabi Orou
    • 4
  1. 1.Department of Mechanical, Petroleum and Gas Engineering, Faculty of Mines and Petroleum IndustriesUniversity of MarouaMarouaCameroon
  2. 2.Department of Physics, Higher Teacher Training CollegeUniversity of BamendaBamendaCameroon
  3. 3.Department of Telecommunication and Network Engineering, IUT-Fotso Victor of BandjounUniversity of DschangBandjounCameroon
  4. 4.Institut de Mathématiques et de Sciences PhysiquesUniversité d’Abomey-CalaviPorto NovoBenin

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