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Abrupt change of synchronization of ring coupled Duffing oscillator

Wu Yong-Feng Zhang Shi-Ping Sun Jin-Wei Peter Rolfe

Abrupt change of synchronization of ring coupled Duffing oscillator

Wu Yong-Feng, Zhang Shi-Ping, Sun Jin-Wei, Peter Rolfe
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  • The ring coupled Duffing oscillator was investigated, a phenomenon was observed when analyzing the synchronization evolution between coupled oscillators, which shows that if all oscillators are driven by the same periodic driving force,the motion trajectory between weakly coupled oscillators will generate two abrupt changes from synchronization to non-synchronization and then to synchronization in the phase transition of period-doubling bifurcation, chaotic state and large-scale periodic state. Any synchronous abrupt change can be used to rapidly identify system phase transition, and thus a weak periodic signal detection method was proposed based on the phase transition of period-doubling bifurcation and chaotic state.
    • Funds:
    [1]

    Birx D I 1992 IEEE Int. Joint Conf. Neural Networks 22 881

    [2]

    Wang G Y, Tao G L, Chen X, Lin J Y 1997 Chinese Journal of Scientific Instrument 18 209 (in Chinese) [王冠宇、陶国良、陈 行、林建亚 1997 仪器仪表学报 18 209]

    [3]

    Li Y, Yang B J, Lin H B, Liu X H 2005 Acta Phys. Sin. 54 1994 (in Chinese) [李 月、杨宝俊、林红波、刘晓华 2005 物 理学报 54 1994] 〖4] Yuan Y, Li Y, Danilo P M, Yang B J 2009 Chin. Phys. B 18 0958

    [4]

    Wang Y C, Zhao Q C, Wang A B 2008 Chin. Phys. B 17 2373

    [5]

    Li Y, Yang B J, Yuan Y, Liu X H 2007 Chin. Phys. 16 1072

    [6]

    Zhai D Q, Liu C X, Liu Y, Xu Z 2010 Acta Phys. Sin. 59 0816 (in Chinese) [翟笃庆、刘崇新、刘 尧、许 喆 2010 物理学报 59 0816]

    [7]

    Xiang X Q, Shi B C 2010 Chaos 20 013104

    [8]

    Li Y, Yang B J, Deng X Y 2004 Chin. Phys. 13 1368

    [9]

    Li Y, Xu K, Yang B J, Yuan Y 2008 Acta Phys. Sin. 57 3353 (in Chinese) [李 月、徐 凯、杨宝俊、袁 野 2008 物理学报 57 3353]

    [10]

    Wang Y S, Jiang W Z, Zhao J J, Fan H D 2008 Acta Phys. Sin. 57 2053 (in Chinese) [王永生、姜文志、赵建军、范洪达 2008 物理学报 57 2053]

    [11]

    Li Y, Lu P, Yang B J, Zhao X P 2006 Acta Phys. Sin. 55 1672 (in Chinese) [李 月、路 鹏、杨宝俊、赵雪平 2006 物理学报 55 1672]

    [12]

    Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821

    [13]

    Yanchuka S, Maistrenko Y, Mbsekilde E 2003 Chaos 13 388

    [14]

    Guan S G, Li K, Lai C H 2006 Chaos 16 023107

    [15]

    Hu J, Zhang Q J 2008 Chin. Phys. B 17 503

    [16]

    Ren H P, Han C Z, Liu D 2008 Chin. Phys. B 17 1202

    [17]

    Zhu S Q, Luo X Q, Fang J X 2001 Chin. Phys. Lett. 18 727

    [18]

    Li G H, Xu D M, Zhou S P 2004 Acta Phys. Sin. 53 706 (in Chinese) [李国辉、徐得名、周世平 2004 物理学报 53 706]

    [19]

    Qin W Y, Wang H J, Gao H S 2008 Acta Phys. Sin. 57 42 (in Chinese) [秦卫阳、王红瑾、高行山 2008 物理学报 57 42]

    [20]

    Liu Z H, Chen S G, Hu B 1999 Phys. Rev. E 59 2817

    [21]

    Wang T B, Qin T F, Chen G Z 2001 Acta Phys. Sin. 50 1851 (in Chinese) [王铁邦、覃团发、陈光旨 2001 物理学报 50 1851]

    [22]

    Qian Y, Song X Y, Shi W, Chen G Z, Xue Y 2006 Acta Phys. Sin. 55 4420 (in Chinese) [钱 郁、宋宣玉、时 伟、陈光旨、薛 郁 2006 物理学报 55 4420]

  • [1]

    Birx D I 1992 IEEE Int. Joint Conf. Neural Networks 22 881

    [2]

    Wang G Y, Tao G L, Chen X, Lin J Y 1997 Chinese Journal of Scientific Instrument 18 209 (in Chinese) [王冠宇、陶国良、陈 行、林建亚 1997 仪器仪表学报 18 209]

    [3]

    Li Y, Yang B J, Lin H B, Liu X H 2005 Acta Phys. Sin. 54 1994 (in Chinese) [李 月、杨宝俊、林红波、刘晓华 2005 物 理学报 54 1994] 〖4] Yuan Y, Li Y, Danilo P M, Yang B J 2009 Chin. Phys. B 18 0958

    [4]

    Wang Y C, Zhao Q C, Wang A B 2008 Chin. Phys. B 17 2373

    [5]

    Li Y, Yang B J, Yuan Y, Liu X H 2007 Chin. Phys. 16 1072

    [6]

    Zhai D Q, Liu C X, Liu Y, Xu Z 2010 Acta Phys. Sin. 59 0816 (in Chinese) [翟笃庆、刘崇新、刘 尧、许 喆 2010 物理学报 59 0816]

    [7]

    Xiang X Q, Shi B C 2010 Chaos 20 013104

    [8]

    Li Y, Yang B J, Deng X Y 2004 Chin. Phys. 13 1368

    [9]

    Li Y, Xu K, Yang B J, Yuan Y 2008 Acta Phys. Sin. 57 3353 (in Chinese) [李 月、徐 凯、杨宝俊、袁 野 2008 物理学报 57 3353]

    [10]

    Wang Y S, Jiang W Z, Zhao J J, Fan H D 2008 Acta Phys. Sin. 57 2053 (in Chinese) [王永生、姜文志、赵建军、范洪达 2008 物理学报 57 2053]

    [11]

    Li Y, Lu P, Yang B J, Zhao X P 2006 Acta Phys. Sin. 55 1672 (in Chinese) [李 月、路 鹏、杨宝俊、赵雪平 2006 物理学报 55 1672]

    [12]

    Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821

    [13]

    Yanchuka S, Maistrenko Y, Mbsekilde E 2003 Chaos 13 388

    [14]

    Guan S G, Li K, Lai C H 2006 Chaos 16 023107

    [15]

    Hu J, Zhang Q J 2008 Chin. Phys. B 17 503

    [16]

    Ren H P, Han C Z, Liu D 2008 Chin. Phys. B 17 1202

    [17]

    Zhu S Q, Luo X Q, Fang J X 2001 Chin. Phys. Lett. 18 727

    [18]

    Li G H, Xu D M, Zhou S P 2004 Acta Phys. Sin. 53 706 (in Chinese) [李国辉、徐得名、周世平 2004 物理学报 53 706]

    [19]

    Qin W Y, Wang H J, Gao H S 2008 Acta Phys. Sin. 57 42 (in Chinese) [秦卫阳、王红瑾、高行山 2008 物理学报 57 42]

    [20]

    Liu Z H, Chen S G, Hu B 1999 Phys. Rev. E 59 2817

    [21]

    Wang T B, Qin T F, Chen G Z 2001 Acta Phys. Sin. 50 1851 (in Chinese) [王铁邦、覃团发、陈光旨 2001 物理学报 50 1851]

    [22]

    Qian Y, Song X Y, Shi W, Chen G Z, Xue Y 2006 Acta Phys. Sin. 55 4420 (in Chinese) [钱 郁、宋宣玉、时 伟、陈光旨、薛 郁 2006 物理学报 55 4420]

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  • Received Date:  06 May 2010
  • Accepted Date:  27 May 2010
  • Published Online:  15 February 2011

Abrupt change of synchronization of ring coupled Duffing oscillator

  • 1. School of Electrical Engineering and Automation, Harbin Institute of Technology, Harbin 150001, China

Abstract: The ring coupled Duffing oscillator was investigated, a phenomenon was observed when analyzing the synchronization evolution between coupled oscillators, which shows that if all oscillators are driven by the same periodic driving force,the motion trajectory between weakly coupled oscillators will generate two abrupt changes from synchronization to non-synchronization and then to synchronization in the phase transition of period-doubling bifurcation, chaotic state and large-scale periodic state. Any synchronous abrupt change can be used to rapidly identify system phase transition, and thus a weak periodic signal detection method was proposed based on the phase transition of period-doubling bifurcation and chaotic state.

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