Please wait a minute...
Chin. Phys. B, 2020, Vol. 29(12): 120501    DOI: 10.1088/1674-1056/aba9cd
GENERAL Prev   Next  

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
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.
Keywords:  nonlinear resonances      hysteresis and jump phenomena      modified Josephson junction  
Received:  04 May 2020      Revised:  11 July 2020      Accepted manuscript online:  28 July 2020
PACS:  05.45.-a (Nonlinear dynamics and chaos)  
  03.75.Lm (Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices, and topological excitations)  
Corresponding Authors:  Corresponding author. E-mail:   

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

[1] Siewe M S, Tchawoua C and Rajasekar S Commun. Nonlinear Sci. Numer. Simul. 17 4485 DOI: 10.1016/j.cnsns.2012.02.0302012
[2] Miwadinou C H, Monwanou A V and Orou J B C Int. J. Bifur. Chaos 25 1550024 DOI: 10.1142/S02181274155002482015
[3] Strogatz S2001 Nonlinear Dynamics And Chaos: With Applications To Physics, Biology, Chemistry, And Engineering (Studies in Nonlinearity)(Westview Press)
[4] Monwanou A V, Miwadinou C H, Hinvi L and Orou J B C2017 Int. J. Sci. Eng. Appl. Sci. 88 97 ISBN: 2395-3470
[5] Pandey M, Rand R H and Zehnder A T 2007 International Design Engineering Technical Conferences paper No. DETC2007-34411, pp. 893-903 DOI: 10.1115/detc2007-34411
[6] Bi Q Int. J. NonLinear Mech. 39 33 DOI: 10.1016/S0020-7462(02)00126-92004
[7] Li S, Niu J and Li X Chin. Phys. B 27 120502 DOI: 10.1088/1674-1056/27/12/1205022018
[8] Mitsi S, Natsiavas S and Tsiafis I Nonlinear Dyn. 16 23 DOI: 10.1023/A:10082641042381998
[9] Natsiavas S 1994 Nonlinear Dyn. 6 69 DOI: 10.1007/BF00045433
[10] Nayfeh A H2011 Introduction to perturbation techniques (John Wiley and Sons)
[11] Mishra A, Saha S, Hens C, Roy P K, Bose M, Louodop H, Cerdeira H A and Dana S K Phys. Rev. E 95 010201 DOI: 10.1103/PhysRevE.95.0102012017
[12] Domínguez D and Cerdeira H A Phys. Rev. B 52 513 DOI: 10.1103/PhysRevB.52.5131995
[13] Domínguez D and Cerdeira H A 1995 Phys. Lett. A 200 43 DOI: 10.1016/0375-9601(95)00172-y
[14] Domínguez and Cerdeira H A Phys. Rev. Lett. 71 3359 DOI: 10.1103/PhysRevLett.71.33591993
[15] Tang J S, Fu W B and Li K A Chin. Phys. 11 1004 DOI: 10.1088/1009-1963/11/10/3062002
[16] Levi M, Hoppensteadt F C and Miranker W L Q. Appl Math. 36 167 DOI: 10.1090/qam/1978-36-021978
[17] Josephson B 1962 Phys. Lett. 1 251 DOI: 10.1016/0031-9163(62)91369-0
[18] Zharkov G and Altudov Y K1978 Sov. Phys. JETP 47 901
[19] Tsang K Y and Schwartz I B Phys. Rev. Lett. 68 2265 DOI: 10.1103/PhysRevLett.68.22651992
[20] Duwel A E, Watanabe S, Triá E, Orlando T P, van der Zant H S J and Strogatz S H J. Appl. Phys. 82 4661 DOI: 10.1063/1.3662051997
[21] Duwel A E, Triá E, Orlando T P, van der Zant H S J, Watanabe S and Strogatz S H J. Appl. Phys. 79 7864 DOI: 10.1063/1.3623961996
[22] Goldobin E, Koelle D, Kleiner R and Buzdin A Phys. Rev. B 76 224523 DOI: 10.1103/PhysRevB.76.2245232007
[23] Krantz P, Reshitnyk Y, Wustmann W, Bylander J, Gustavsson S, Oliver W D, Duty T, Shumeiko V and Delsing P New J. Phys. 15 105002 DOI: 10.1088/1367-2630/15/10/1050022013
[24] Louodop P, Tchitnga R, Fagundes F F, Kountchou M, Tamba V K, Carlos L P L and Cerdeira H A 2019 Phys. Rev. E 99 105002 DOI: 10.1103/PhysRevE.99.042208
[25] You J Q and Nori F Nature 474 589 DOI: 10.1038/nature101222011
[26] Kaplunenko V and Fischer G M 2004 Supercond. Sci. Technol. 17 S145 DOI: 10.1088/0953-2048/17/5/011
[27] Chen M, Xu Q, Lin Y and Bao B Nonlinear Dyn. 87 789 DOI: 10.1007/s11071-016-3077-62016
[28] Xu Q, Zhang Q, Qian H, Wu H and Bao B Int. J. Cir. Theor. Appl. 46 1917 DOI: 10.1002/cta.v46.102018
[29] Bao B, Luo J, Bao H, Chen C, Wu H and Xu Q Int. J. Bifur. Chaos 29 1950168 DOI: 10.1142/S02181274195016822019
[30] Luo J, Bao H, Chen M, Xu Q and Bao B Eur. Phys. J. S. T. 228 1983 DOI: 10.1140/epjst/e2019-800235-62019
[31] Han X, Chen Z and Bi Q Chaos 26 023117 DOI: 10.1063/1.49425032016
[32] Xu Q, Zhang Q, Bao B and Hu Y 2017 IEEE 5 21039 DOI: 10.1109/access.2017.2727522
[1] An incommensurate fractional discrete macroeconomic system: Bifurcation, chaos, and complexity
Abderrahmane Abbes, Adel Ouannas, and Nabil Shawagfeh. Chin. Phys. B, 2023, 32(3): 030203.
[2] A color image encryption algorithm based on hyperchaotic map and DNA mutation
Xinyu Gao(高昕瑜), Bo Sun(孙博), Yinghong Cao(曹颖鸿), Santo Banerjee, and Jun Mou(牟俊). Chin. Phys. B, 2023, 32(3): 030501.
[3] Realizing reliable XOR logic operation via logical chaotic resonance in a triple-well potential system
Huamei Yang(杨华美) and Yuangen Yao(姚元根). Chin. Phys. B, 2023, 32(2): 020501.
[4] Epilepsy dynamics of an astrocyte-neuron model with ammonia intoxication
Zhixuan Yuan(袁治轩), Mengmeng Du(独盟盟), Yangyang Yu(于羊羊), and Ying Wu(吴莹). Chin. Phys. B, 2023, 32(2): 020502.
[5] Memristor hyperchaos in a generalized Kolmogorov-type system with extreme multistability
Xiaodong Jiao(焦晓东), Mingfeng Yuan(袁明峰), Jin Tao(陶金), Hao Sun(孙昊), Qinglin Sun(孙青林), and Zengqiang Chen(陈增强). Chin. Phys. B, 2023, 32(1): 010507.
[6] Resonance and antiresonance characteristics in linearly delayed Maryland model
Hsinchen Yu(于心澄), Dong Bai(柏栋), Peishan He(何佩珊), Xiaoping Zhang(张小平), Zhongzhou Ren(任中洲), and Qiang Zheng(郑强). Chin. Phys. B, 2022, 31(12): 120502.
[7] A novel hyperchaotic map with sine chaotification and discrete memristor
Qiankun Sun(孙乾坤), Shaobo He(贺少波), Kehui Sun(孙克辉), and Huihai Wang(王会海). Chin. Phys. B, 2022, 31(12): 120501.
[8] Finite-time synchronization of uncertain fractional-order multi-weighted complex networks with external disturbances via adaptive quantized control
Hongwei Zhang(张红伟), Ran Cheng(程然), and Dawei Ding(丁大为). Chin. Phys. B, 2022, 31(10): 100504.
[9] Periodic and chaotic oscillations in mutual-coupled mid-infrared quantum cascade lasers
Zhi-Wei Jia(贾志伟), Li Li(李丽), Yi-Yan Guo(郭一岩), An-Bang Wang(王安帮), Hong Han(韩红), Jin-Chuan Zhang(张锦川), Pu Li(李璞), Shen-Qiang Zhai(翟慎强), and Feng-Qi Liu(刘峰奇). Chin. Phys. B, 2022, 31(10): 100505.
[10] Exponential sine chaotification model for enhancing chaos and its hardware implementation
Rui Wang(王蕊), Meng-Yang Li(李孟洋), and Hai-Jun Luo(罗海军). Chin. Phys. B, 2022, 31(8): 080508.
[11] Characteristics of piecewise linear symmetric tri-stable stochastic resonance system and its application under different noises
Gang Zhang(张刚), Yu-Jie Zeng(曾玉洁), and Zhong-Jun Jiang(蒋忠均). Chin. Phys. B, 2022, 31(8): 080502.
[12] Synchronously scrambled diffuse image encryption method based on a new cosine chaotic map
Xiaopeng Yan(闫晓鹏), Xingyuan Wang(王兴元), and Yongjin Xian(咸永锦). Chin. Phys. B, 2022, 31(8): 080504.
[13] Effect of astrocyte on synchronization of thermosensitive neuron-astrocyte minimum system
Yi-Xuan Shan(单仪萱), Hui-Lan Yang(杨惠兰), Hong-Bin Wang(王宏斌), Shuai Zhang(张帅), Ying Li(李颖), and Gui-Zhi Xu(徐桂芝). Chin. Phys. B, 2022, 31(8): 080507.
[14] Research and application of stochastic resonance in quad-stable potential system
Li-Fang He(贺利芳), Qiu-Ling Liu(刘秋玲), and Tian-Qi Zhang(张天骐). Chin. Phys. B, 2022, 31(7): 070503.
[15] Design and FPGA implementation of a memristor-based multi-scroll hyperchaotic system
Sheng-Hao Jia(贾生浩), Yu-Xia Li(李玉霞), Qing-Yu Shi(石擎宇), and Xia Huang(黄霞). Chin. Phys. B, 2022, 31(7): 070505.
No Suggested Reading articles found!