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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.
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Keywords:
- Josephson junction /
- linear delayed feedback /
- Hopf bifurcation /
- chaos
[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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[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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