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Nonlinear resonances phenomena in a modified Josephson junction model |
| Pernel Nguenang1, Sandrine Takam Mabekou2, Patrick Louodop1,3, Arthur Tsamouo Tsokeng1, and Martin Tchoffo1,† |
| 1 Research Unit Condensed Matter, Electronics and Signal Processing, The University of Dschang, P. O. Box 67 Dschang, Cameroon; 2 Unitè de Recherche de Mècanique et de Modèlisation des Syst\`emes Physiques (UR-2MSP), Facultè des Sciences, Universitè de Dschang, BP 69 Dschang, Cameroun; 3 S\ ao Paulo State University (UNESP), Instituto de Fìsica Teórica, Rua Dr. Bento, Teobaldo Ferraz 271, Bloco II, Barra Funda, 01140-070 S\ ao Paulo, Brazil |
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Abstract In this paper, the equivalent circuit of the non-autonomous Josephson junction (JJ) is presented and the effect of the proper frequency on the phase φ is studied. We also study nonlinear resonance phenomena in the oscillations of a modified Josephson junction (MJJ). These oscillations are probed through a system of nonlinear differential equations and the multiple time scale method is employed to investigate all different types of resonance that occur. The results of primary, superharmonic and subharmonic resonances are obtained analytically. We show that the system exhibits hardening and softening behaviors, as well as hysteresis and amplitude hopping phenomena in primary and superharmonic resonances, and only the hysteresis phenomenon in subharmonic resonance. In addition, the stabilities and the steady state solutions in each type of resonances are kindly evaluated. The number of equilibrium points that evolve with time and their stabilities are also studied. Finally, the equations of motion are numerically integrated to check the correctness of analytical calculations. We further show that the dynamics of the MJJ is strongly influenced by its parameters.
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Received: 04 May 2020
Revised: 11 July 2020
Accepted manuscript online: 28 July 2020
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PACS:
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05.45.-a
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(Nonlinear dynamics and chaos)
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03.75.Lm
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(Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices, and topological excitations)
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Corresponding Authors:
†Corresponding author. E-mail: mtchoffo2000@yahoo.fr
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Cite this article:
Pernel Nguenang, Sandrine Takam Mabekou, Patrick Louodop, Arthur Tsamouo Tsokeng, and Martin Tchoffo Nonlinear resonances phenomena in a modified Josephson junction model 2020 Chin. Phys. B 29 120501
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