线性延时反馈Josephson结的Hopf分岔和混沌化

张立森; 蔡理; 冯朝文

doi:10.7498/aps.60.060306

摘要

考虑线性延时反馈控制下电阻-电容分路的Josephson结,运用非线性动力学理论分析了受控系统平凡解的稳定性.理论分析表明,随着控制参数的改变,系统的稳定平凡解将会通过Hopf分岔失稳,并推导了发生Hopf分岔的临界参数条件.对不同参数条件下受控系统的动力学进行了数值分析.结果显示,系统由Hopf分岔产生的稳定周期解,将进一步通过对称破缺分岔和倍周期分岔通向混沌.

关键词:

In this paper, a resistive-capacitive-shunted Josephson junction with linear delayed feedback is considered. The stability of trivial solution of the controlled system is analyzed using nonlinear dynamics theory, and the theoretical results show that the stable trivial solution of the system will lose its stability via Hopf bifurcation as control parameter varies. The critical parameter condition of Hopf bifurcation is also derived. Numerical analysis of the controlled system is carried out under different parameter conditions, and the results show that the stable periodic solution generated by supercritical Hopf bifurcation may transit to chaos gradually through a process of symmetry-breaking bifurcation and period-doubling bifurcation.

Keywords:

作者及机构信息

1.
空军工程大学理学院,西安 710051

基金项目: 国家高技术研究发展计划(批准号:2008AAJ225)和空军工程大学研究生科技创新计划(批准号:Dx2010405)资助的课题.

Authors and contacts

1.
School of Science, Air Force Engineering University, Xi’ an 710051, China

参考文献

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[7]	Octavio M 1984 Phys. Rev. B 29 1231
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[11]	Zhang L S, Cai L, Feng C W 2010 Acta Elec. Sin. 38 1311 (in Chinese) [张立森、蔡理、冯朝文 2010 电子学报 38 1311]
[12]	Zhang L S, Cai L, Feng C W 2011 Acta Phys. Sin. 60 030308 (in Chinese) [张立森、蔡理、冯朝文 2011 物理学报 60 030308]
[13]	Feng Y L, Shen K 2008 Chin. Phys. B 17 111
[14]	Vincent U E, Ucar A, Laoye J A, Kareem S O 2008 Physica C 468 374
[15]	Njah A N, Ojo K S, Adebayo G A, Obawole A O 2010 Physica C 470 558
[16]	Chen G, Lai D 1998 Int. J. Bifur. Chaos 8 1585
[17]	Wang X F, Chen G, Yu X 2000 Chaos 10 771
[18]	Wang X F, Chen G 2003 IEEE Trans. Circ. Syst.Ⅰ 50 812
[19]	Ren H P, Liu D, Han C Z 2006 Acta Phys. Sin. 55 2694 (in Chinese) [任海鹏、刘丁、韩崇昭 2006 物理学报 55 2694]
[20]	Pyragas K 1992 Phys. Lett. A 170 421
[21]	Nayak C R, Kuriakose V C 2008 Chaos 18 023129
[22]	Belair J, Campbell S A 1994 SIAM J. Appl. Math. 54 1402
[23]	Liu C X 2007 Nonlinear Circuit Theory and its Applications (Xi’an: Xi’an Jiaotong University Press) p98 (in Chinese) [刘崇新 2007 非线性电路理论及应用(西安: 西安交通大学出版社) 第98页]

施引文献

[1]	Winkler D 2003 Supercond. Sci. Technol. 16 1583
[2]	Chiorescu I, Nakamura Y, Harmans C J P M, Mooij J E 2003 Science 299 1869
[3]	Bens S P, Hamilton C A 2004 Proc. IEEE 92 1617
[4]	Golod T, Rydh A, Krasnov V M 2010 Physica C 470 890
[5]	Nayak C R, Kuriakose V C 2008 Chaos 18 013125
[6]	Huberman B A, Crutchfield J P, Packard N H 1980 Appl. Phys. Lett. 37 750
[7]	Octavio M 1984 Phys. Rev. B 29 1231
[8]	Wang Z Y, Liao H Y, Zhou S P 2001 Acta Phys. Sin. 50 1996 (in Chinese) [王震宇、廖红印、周世平 2001 物理学报 50 1996]
[9]	Dana S K, Sengupta D C, Edoh K D 2001 IEEE Trans. Circ. Syst.Ⅰ 48 990
[10]	Lei Y M, Xu W 2008 Acta Phys. Sin. 57 3342 (in Chinese) [雷佑铭、徐伟 2008 物理学报 57 3342]
[11]	Zhang L S, Cai L, Feng C W 2010 Acta Elec. Sin. 38 1311 (in Chinese) [张立森、蔡理、冯朝文 2010 电子学报 38 1311]
[12]	Zhang L S, Cai L, Feng C W 2011 Acta Phys. Sin. 60 030308 (in Chinese) [张立森、蔡理、冯朝文 2011 物理学报 60 030308]
[13]	Feng Y L, Shen K 2008 Chin. Phys. B 17 111
[14]	Vincent U E, Ucar A, Laoye J A, Kareem S O 2008 Physica C 468 374
[15]	Njah A N, Ojo K S, Adebayo G A, Obawole A O 2010 Physica C 470 558
[16]	Chen G, Lai D 1998 Int. J. Bifur. Chaos 8 1585
[17]	Wang X F, Chen G, Yu X 2000 Chaos 10 771
[18]	Wang X F, Chen G 2003 IEEE Trans. Circ. Syst.Ⅰ 50 812
[19]	Ren H P, Liu D, Han C Z 2006 Acta Phys. Sin. 55 2694 (in Chinese) [任海鹏、刘丁、韩崇昭 2006 物理学报 55 2694]
[20]	Pyragas K 1992 Phys. Lett. A 170 421
[21]	Nayak C R, Kuriakose V C 2008 Chaos 18 023129
[22]	Belair J, Campbell S A 1994 SIAM J. Appl. Math. 54 1402
[23]	Liu C X 2007 Nonlinear Circuit Theory and its Applications (Xi’an: Xi’an Jiaotong University Press) p98 (in Chinese) [刘崇新 2007 非线性电路理论及应用(西安: 西安交通大学出版社) 第98页]

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