摘要 Collective synchronization is investigated on the small-world network (NW model). The order parameter is introduced to measure the synchronization of phase. It is found that there are differences between the processes of synchronization and desynchronization. The dependence of order parameter on the coupling strength is shown like a hysteresis loop. The size of the loop demonstrates the non-monotonicity with the change of adding probability, and is relevant to the construction of the network. The area may be maximum, as the adding probability is equal to 0.4. This phenomenon indicates that the clusters in the network play an important role in the processes of synchronization and desynchronization
Abstract： Collective synchronization is investigated on the small-world network (NW model). The order parameter is introduced to measure the synchronization of phase. It is found that there are differences between the processes of synchronization and desynchronization. The dependence of order parameter on the coupling strength is shown like a hysteresis loop. The size of the loop demonstrates the non-monotonicity with the change of adding probability, and is relevant to the construction of the network. The area may be maximum, as the adding probability is equal to 0.4. This phenomenon indicates that the clusters in the network play an important role in the processes of synchronization and desynchronization
MA Pei-Jie;WANG Bing-Hong. Order Parameter Hysteresis on the Complex Network[J]. 中国物理快报, 2008, 25(9): 3507-3510.
MA Pei-Jie, WANG Bing-Hong. Order Parameter Hysteresis on the Complex Network. Chin. Phys. Lett., 2008, 25(9): 3507-3510.
[1] Heagy J F, Carroll T L and Pecora L M 1994 Phys.Rev. E 50 1874 [2] Wu C W and Chua L O 1995 IEEE Trans. Circuits Syst.I 42 430. [3] Albert R and Barab\'{asi A L 2002 Rev. Mod. Phys. 74 47 [4 Dorogovtsev S N and Mendes J F F 2002 Adv. Phys. 51 1079 [5] Newman M E J 2003 SIAM Rev. 45 167 [6] Boccaletti S, Latora V, Moreno Y, Chavez M and Hwang D U2006 Phys. Rep. 424 175 [7] Gade P M and Hu C K 2002 Phys. Rev. E 62 6409 [8] Hasegawa H 2004 Phys. Rev. E 70 066107 [9] Nishikawa T, Motter A E, Lai Y C and Hoppensteadt F C2003 Phys. Rev. Lett. 91 014101 [10] Zhao M, Zhou T, Wang B H and Wang W X 2005 Phys.Rev. E 72 057102 [11] McGraw P N and Menzinger M 2005 Phys. Rev. E 72 015101(R) [12] Chavez M, Hwang D U, Amann A, Hentschel H G E andBoccaletti S 2005 Phys. Rev. Lett. 94 218701 [13] Chavez M, Hwang D U, Amann A and Boccaletti S 2006 Chaos 16 015106 [14 Zhao M, Zhou T, Wang B H, Ou Q and Ren J 2006 Eur.Phys. J. B 53 (2006) 375 [15] Hong H, Choi M Y and Kim B J 2002 Phys. Rev. E 65 026139 [16] Watte D J and Strogatz S H 1998 Nature 393440 [17] Pecora L M and Carroll T L 1998 Phys. Rev. Lett. 80 2109 [18] Barahona M and Pecora L M, 2002 Phys. Rev. Lett. 89 054101 [19] Pecora L M and Barahona M 2005 Chaos ComplexityLett. 1 61 [20] Kuramoto Y 1984 Chemical Oscillations, Wave andTurbulence (Berlin: Springer) [21] Pikovsky A 2001 Synchronization (Cambridge:Cambridge University Press)
2008, Vol. 25 
