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The present paper aims to investigate the phase synchronization in chaotic oscillator networks by using quantitative indexes. We define two new quantitative indexes, namely the mean phase locking value and mean frequency difference of two adjacent nodes of the network. Lorenz chaotic oscillators with several rotational centers are chosen as networks nodes. We convert the original Lorenz system into the dynamics of amplitude and phase. The chaotic oscillator networks are formed via amplitude coupling. We find that for star-coupled network and small-world network the adjacent oscillation phases are locked. Moreover, phase synchronization definitely comes along with the transition of the mean phase locking value and mean frequency difference by increasing the coupling strength.
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Keywords:
- dynamical network /
- phase synchronization /
- mean phase locking value /
- mean frequency difference
[1] Shabunin A,Astakhov V,Kurths J 2005 Phys. Rev. E 72 016218
[2] Quiroga R Q,Kraskov A,Kreuz T,Grassberger P 2002 Phys. Rev. E 65 041903
[3] Schiff S J,So P,Chang T 1996 Phys. Rev. E 54 708
[4] Arnhold J,Grassberger P,Lehnertz K,Elger C E 1999 Physica D 134 419
[5] Schmitz A 2000 Phys. Rev. E 62 7508
[6] Kramer M A,Edwards E,Soltani M,Berger M,Knight R,Szeri A J 2004 Phys. Rev. E 70 011914
[7] Romano M C,Thiel M,Kurths J,Bloh V W 2004 Phys. Lett. A 330 214
[8] Anishchenko V S,Astakhov A A,Nikolaev V V,Shabunin A V 2000 J. Commun. Technol. & Electron. 45 179
[9] Shabunin A,Astakhov V,Anishchenko V S 2002 Int. J. Bifurc. Chaos 12 1895
[10] Schfer C,Rosenblum M G,Kurths J,Abel H H 1998 Nature (London) 392 239
[11] Schfer C,Rosenblum M G,Abel H H,Kurths J 1999 Phys. Rev. E 60 857
[12] Tass P,Rosenblum M G,Weule J,Kurths J,Pikovsky A,Volkmann J,Schnitzler A,Freund A 1998 Phys. Rev. Lett. 81 3291
[13] Lian J,Shuai J,Durand D 2004 J. Neural. Eng. 1 46
[14] Stefanovska A,Haken H,McClintock P V E,Hozic M,Bajrovic F,Ribaric S 2000 Phys. Rev. Lett. 85 4831
[15] McClintock P V E,Stefanovska A 2002 Physica A 314 69
[16] Meng J,Wang X Y 2007 Acta. Phys. Sin. 56 5142 (in Chinese) [孟 娟、王兴元 2007 56 5142]
[17] Hao J H,Li W 2005 Acta. Phys. Sin. 54 3491 (in Chinese) [郝建红、李 伟 2005 54 3491]
[18] Hu G,Hu B B,Zheng,Z G,Zhou C S 2000 Acta. Phys. Sin. 49 2320 (in Chinese) [胡 岗、胡斑比、郑志刚、周昌松 2000 49 2320]
[19] Hao J H,Li W 2005 Acta. Phys. Sin. 54 3491 (in Chinese) [郝建红、李 伟 2005 54 3491]
[20] Han F,Lu Q S,Wiercigroch M,Ji Q B 2009 Chin. Phys. B 18 482
[21] Luo X S,Qin Y H,Wei D Q,2009 Chin. Phys. B 18 2184
[22] Liu Y 2009 Acta. Phys. Sin. 58 749 (in Chinese) [刘 勇 2009 58 749]
[23] Xu W,Tang X L 2008 Chin. Phys. B 17 2004
[24] Meinecke F C,Ziehe A,Kurths J,Müller K R 2005 Phys. Rev. Lett. 94 084102
[25] Li C G,Chen G R 2004 Physica A 341 73
[26] Mo X H,Tang G N 2004 Acta. Phys. Sin. 53 2080 (in Chinese) [莫晓华、唐国宁 2004 53 2080]
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[1] Shabunin A,Astakhov V,Kurths J 2005 Phys. Rev. E 72 016218
[2] Quiroga R Q,Kraskov A,Kreuz T,Grassberger P 2002 Phys. Rev. E 65 041903
[3] Schiff S J,So P,Chang T 1996 Phys. Rev. E 54 708
[4] Arnhold J,Grassberger P,Lehnertz K,Elger C E 1999 Physica D 134 419
[5] Schmitz A 2000 Phys. Rev. E 62 7508
[6] Kramer M A,Edwards E,Soltani M,Berger M,Knight R,Szeri A J 2004 Phys. Rev. E 70 011914
[7] Romano M C,Thiel M,Kurths J,Bloh V W 2004 Phys. Lett. A 330 214
[8] Anishchenko V S,Astakhov A A,Nikolaev V V,Shabunin A V 2000 J. Commun. Technol. & Electron. 45 179
[9] Shabunin A,Astakhov V,Anishchenko V S 2002 Int. J. Bifurc. Chaos 12 1895
[10] Schfer C,Rosenblum M G,Kurths J,Abel H H 1998 Nature (London) 392 239
[11] Schfer C,Rosenblum M G,Abel H H,Kurths J 1999 Phys. Rev. E 60 857
[12] Tass P,Rosenblum M G,Weule J,Kurths J,Pikovsky A,Volkmann J,Schnitzler A,Freund A 1998 Phys. Rev. Lett. 81 3291
[13] Lian J,Shuai J,Durand D 2004 J. Neural. Eng. 1 46
[14] Stefanovska A,Haken H,McClintock P V E,Hozic M,Bajrovic F,Ribaric S 2000 Phys. Rev. Lett. 85 4831
[15] McClintock P V E,Stefanovska A 2002 Physica A 314 69
[16] Meng J,Wang X Y 2007 Acta. Phys. Sin. 56 5142 (in Chinese) [孟 娟、王兴元 2007 56 5142]
[17] Hao J H,Li W 2005 Acta. Phys. Sin. 54 3491 (in Chinese) [郝建红、李 伟 2005 54 3491]
[18] Hu G,Hu B B,Zheng,Z G,Zhou C S 2000 Acta. Phys. Sin. 49 2320 (in Chinese) [胡 岗、胡斑比、郑志刚、周昌松 2000 49 2320]
[19] Hao J H,Li W 2005 Acta. Phys. Sin. 54 3491 (in Chinese) [郝建红、李 伟 2005 54 3491]
[20] Han F,Lu Q S,Wiercigroch M,Ji Q B 2009 Chin. Phys. B 18 482
[21] Luo X S,Qin Y H,Wei D Q,2009 Chin. Phys. B 18 2184
[22] Liu Y 2009 Acta. Phys. Sin. 58 749 (in Chinese) [刘 勇 2009 58 749]
[23] Xu W,Tang X L 2008 Chin. Phys. B 17 2004
[24] Meinecke F C,Ziehe A,Kurths J,Müller K R 2005 Phys. Rev. Lett. 94 084102
[25] Li C G,Chen G R 2004 Physica A 341 73
[26] Mo X H,Tang G N 2004 Acta. Phys. Sin. 53 2080 (in Chinese) [莫晓华、唐国宁 2004 53 2080]
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