摘要We study phase synchronization in oscillator networks through phase reduced method. The dynamics of networks is reduced to phase equations by this method. Analysing the phase equations through the master stability function method, one obtains that the oscillators with identical frequency can be in-phase synchronized by weak balanced coupling. Similarly, the problem of frequency synchronization of oscillators with different frequencies is transformed to the existence of a locally asymptotically stable equilibrium of the phase error system.
Abstract：We study phase synchronization in oscillator networks through phase reduced method. The dynamics of networks is reduced to phase equations by this method. Analysing the phase equations through the master stability function method, one obtains that the oscillators with identical frequency can be in-phase synchronized by weak balanced coupling. Similarly, the problem of frequency synchronization of oscillators with different frequencies is transformed to the existence of a locally asymptotically stable equilibrium of the phase error system.
ZHANG Jian-Bao;LIU Zeng-Rong;LI Ying. An Approach to Analyse Phase Synchronization in Oscillator Networks with Weak Coupling[J]. 中国物理快报, 2007, 24(6): 1494-1497.
ZHANG Jian-Bao, LIU Zeng-Rong, LI Ying. An Approach to Analyse Phase Synchronization in Oscillator Networks with Weak Coupling. Chin. Phys. Lett., 2007, 24(6): 1494-1497.
[1] Strogatz S H 2001 Nature 410 268 [2] Shi X and Lu Q S 2007 Chin. Phys. Lett. 24 636 [3] Zhang J, Hou Z and Xin H 2006 Chin. Phys. Lett. 23 2364 [4] Guckenheimer J 1975 J. Math. Biol. 1 259 [5] Kuramoto Y 1984 Chemical Oscillations, Waves andTurbulence (New York: Springer) [6] Winfree A T 1967 J. Theor. Biol. 16 15 [7] Strogatz S H 2000 Physica D 143 1 [8] Li X 2006 Physica D 223 242 [9] Teramae J and Tanaka J 2004 Phys. Rev. Lett. 93 20 [10] Nakao H, Arai K, Nagai K, Yasuhiro T and Kuramoto Y 2005 Phys. Rev. E 72 026220 [11] Pecora L M and Carroll T L 1998 Phys. Rev. Lett. 80 2109 [12] Ermentrout J and Kopell N 1991 J. Math. Biol. 29 195
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