Hyperchaotic behaviours and controlling hyperchaos in an array of RCL-shunted Josephson junctions

doi:10.1088/1674-1056/20/12/120504

中国物理B ›› 2011, Vol. 20 ›› Issue (12): 120504-120504.doi: 10.1088/1674-1056/20/12/120504

Hyperchaotic behaviours and controlling hyperchaos in an array of RCL-shunted Josephson junctions

冯玉玲¹, 姚治海¹, 范健¹, 李日明²

(1)Department of Physics, Science College, Changchun University of Science and Technology, Changchun 130022, China; (2)Department of Physics, Science College, Changchun University of Science and Technology, Changchun 130022, China;Department of Physics, University of Science, Unjong Strict, Pyongyang, DPR Korea

收稿日期:2011-06-13 修回日期:2011-07-13 出版日期:2011-12-15 发布日期:2011-12-15

Hyperchaotic behaviours and controlling hyperchaos in an array of RCL-shunted Josephson junctions

Ri Ilmyong(李日明)^a)b), Feng Yu-Ling(冯玉玲)^a)†, Yao Zhi-Hai(姚治海)^a), and Fan Jian(范健)^a)

^a Department of Physics, Science College, Changchun University of Science and Technology, Changchun 130022, China; ^bDepartment of Physics, University of Science, Unjong Strict, Pyongyang, DPR Korea

Received:2011-06-13 Revised:2011-07-13 Online:2011-12-15 Published:2011-12-15

摘要/Abstract

摘要： This paper deals with dynamical behaviours in an array composed of two resistive-capacitive-inductive-shunted (RCL-shunted) Josephson junctions (RCLSJJs) and a shunted resistor. Numerical simulations show that periodic, chaotic and hyperchaotic states can coexist in this array. Moreover, a scheme for controlling hyperchaos in this array is presented by adjusting the external bias current. Numerical results confirm that this scheme can be effectively used to control hyperchaotic states in this array into stable periodic states, and different stable periodic states with different period numbers can be obtained by appropriately choosing the intensity of the external bias current.

关键词: hyperchaos, controlling hyperchaos, array of RCL-shunted Josephson junctions, Lyapunov exponent

Abstract: This paper deals with dynamical behaviours in an array composed of two resistive-capacitive-inductive-shunted (RCL-shunted) Josephson junctions (RCLSJJs) and a shunted resistor. Numerical simulations show that periodic, chaotic and hyperchaotic states can coexist in this array. Moreover, a scheme for controlling hyperchaos in this array is presented by adjusting the external bias current. Numerical results confirm that this scheme can be effectively used to control hyperchaotic states in this array into stable periodic states, and different stable periodic states with different period numbers can be obtained by appropriately choosing the intensity of the external bias current.

Key words: hyperchaos, controlling hyperchaos, array of RCL-shunted Josephson junctions, Lyapunov exponent

中图分类号: (Numerical simulations of chaotic systems)

05.45.Pq

74.50.+r (Tunneling phenomena; Josephson effects)

李日明, 冯玉玲, 姚治海, 范健. Hyperchaotic behaviours and controlling hyperchaos in an array of RCL-shunted Josephson junctions[J]. 中国物理B, 2011, 20(12): 120504-120504.

Ri Ilmyong(李日明), Feng Yu-Ling(冯玉玲), Yao Zhi-Hai(姚治海), and Fan Jian(范健) . Hyperchaotic behaviours and controlling hyperchaos in an array of RCL-shunted Josephson junctions[J]. Chin. Phys. B, 2011, 20(12): 120504-120504.

参考文献 30

[1]	Benz S P and Buuroughs C 1991 Appl. Phys. Lett. 58 2162
[2]	Whan C B and Lobb C J 1996 Phys. Rev. E 53 405
[3]	Whan C B, Lobb C J and Forrester M G 1995 J. Appl. Phys. 77 382
[4]	Cawthorne A B, Whan C B and Lobb C J 1997 IEEE Trans. Appl. Supercond. 7 2359
[5]	Whan C B and Lobb C J 1996 Phys. Rev. E 53 405
[6]	Cawthorne A B, Whan C B and Lobb C J 1998 J. Appl. Phys. 84 1126
[7]	Cawthorne A B, Barbara P, Shitov S V, Lobb C J, Wiesenfeld K and Zangwill A 1999 Phys. Rev. B 60 7575
[8]	Yang X S and Li Q 2006 Chaos, Solitons and Fractals 27 25
[9]	Dana S K, Roy P K, Sethia G C, Sen A and Sengupta D C 2006 IEEE Proc. Circ. Dev. Syst. 153 453
[1]	Ucar A, Lonngren K E and Bai E W 2007 Chaos, Solitons and Fractals 31 105
[11]	Feng Y L and Shen K 2008 Chin. Phys. B 17 111
[12]	Feng Y L, Zhang X H, Jiang Z G and Shen K 2010 Int. J. Mod. Phys. B 24 5675
[13]	Feng Y L and Shen K 2008 Eur. Phys. J. B 61 105
[14]	Feng Y L and Shen K 2008 Chin. Phys. B 17 550
[15]	Feng Y L, Zhang X H, Jiang Z G and Shen K 2009 Int. J. Mod. Phys. B 23 3601
[16]	Feng Y L and Shen K 2010 Chin. J. Phys. 48 316
[17]	Basler M, Krech W and Platov K Y 1995 Phys. Rev. B 52 7504
[18]	Hassel J, Gronberg L, Helisto P and Seppa H 2006 Appl. Phys. Lett. 89 072503
[19]	Grib A N, Seidel P and Scherbel J 2001 Phys. Rev. B 65 094508
[20]	Bhagavatula R, Ebner C and Jayaprakash C 1994 Phys. Rev. B 50 9376
[21]	Chernikov A A and Schmidt G 1994 Phys. Rev. E 50 3436
[22]	Zhou T G, Mao J, Liu T S, Lai Y and Yan S L 2009 Chin. Phys. Lett. 26 077401
[23]	Klushin A M, He M, Yan S L and Klein N 2006 Appl. Phys. Lett. 89 232505
[24]	Zhou T G, Yan S L, Zou X, Li S, Ji L and Zhao X J 2006 Chin. Phys. Lett. 23 1935
[25]	Zhang S H and Shen K 2003 Chin. Phys. 12 149
[26]	Feng X Q, Yao Z H, Tian Z L and Han X Y 2010 Acta Phys. Sin. 59 8414 (in Chinese)
[27]	Wolf A, Swift J B, Swinney H L and Vastano J A 1985 Physica D 16 285
[28]	Sprott J C 1997 Phys. Lett. A 228 271
[29]	Hadley P and Beasley M R 1987 Appl. Phys. Lett. 50 621
[30]	Hu G, Xiao J H and Zheng Z G 2000 Chaos Control (Shanghai: Shanghai Scientific and Technological Education Publishing House) pp.~54--57

[1]	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). Memristor hyperchaos in a generalized Kolmogorov-type system with extreme multistability[J]. 中国物理B, 2023, 32(1): 10507-010507.
[2]	Jianing Dong(董佳宁), Yang Xiang(向阳), Hong Liu(刘洪), and Suyang Qin(秦苏洋). Effect of pressure evolution on the formation enhancement in dual interacting vortex rings[J]. 中国物理B, 2022, 31(8): 84701-084701.
[3]	Sixiao Kong(孔思晓), Chunbiao Li(李春彪), Shaobo He(贺少波), Serdar Çiçek, and Qiang Lai(赖强). A memristive map with coexisting chaos and hyperchaos[J]. 中国物理B, 2021, 30(11): 110502-110502.
[4]	李山, 姜楠, 杨绍琼, 黄永祥, 吴彦华. Coherent structures over riblets in turbulent boundary layer studied by combining time-resolved particle image velocimetry (TRPIV), proper orthogonal decomposition (POD), and finite-time Lyapunov exponent (FTLE)[J]. 中国物理B, 2018, 27(10): 104701-104701.
[5]	雷佑铭, 张红霞. Homoclinic and heteroclinic chaos in nonlinear systems driven by trichotomous noise[J]. 中国物理B, 2017, 26(3): 30502-030502.
[6]	吴浩, 侯威, 颜鹏程, 张志森, 王阔. A study of the early warning signals of abrupt change in the Pacific decadal oscillation[J]. 中国物理B, 2015, 24(8): 89201-089201.
[7]	李梦平, 许雪梅, 杨兵初, 丁家峰. A circular zone counting method of identifying a Duffing oscillator state transition and determining the critical value in weak signal detection[J]. 中国物理B, 2015, 24(6): 60504-060504.
[8]	曹绿晨, 罗玉玲, 丘森辉, 刘俊秀. A perturbation method to the tent map based on Lyapunov exponent and its application[J]. 中国物理B, 2015, 24(10): 100501-100501.
[9]	李天增, 王瑜, 罗懋康. Control of fractional chaotic and hyperchaotic systems based on a fractional order controller[J]. , 2014, 23(8): 80501-080501.
[10]	Hamid Reza Abbasi, Ahmad Gholami, Seyyed Hamid Fathi, Ataollah Abbasi. Effect of metal oxide arrester on the chaotic oscillations in the voltage transformer with nonlinear core loss model using chaos theory[J]. Chin. Phys. B, 2014, 23(1): 18201-018201.
[11]	Paulo C. Rech. The dynamics of a symmetric coupling of three modified quadratic maps[J]. 中国物理B, 2013, 22(8): 80202-080202.
[12]	张勇. New predication of chaotic time series based on local Lyapunov exponent[J]. 中国物理B, 2013, 22(5): 50502-050502.
[13]	周继超, Hyunsik Son, Namtae Kim, Han Jung Song. Stability of operation versus temperature of a three-phase clock-driven chaotic circuit[J]. 中国物理B, 2013, 22(12): 120506-120506.
[14]	朱大锐, 刘崇新, 燕并男. Controlling and synchronization of a hyperchaotic system based on passive control[J]. 中国物理B, 2012, 21(9): 90509-090509.
[15]	刘文波, 邓榤生, 陈关荣. Forming and implementing a hyperchaotic system with rich dynamics[J]. 中国物理B, 2011, 20(9): 90510-090510.

Hyperchaotic behaviours and controlling hyperchaos in an array of RCL-shunted Josephson junctions

Hyperchaotic behaviours and controlling hyperchaos in an array of RCL-shunted Josephson junctions

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 30

相关文章 15

Metrics

本文评价

推荐阅读 0