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Measure synchronization is an interesting phenomenon found in coupled Hamiltonian systems. By taking Poincaré section analysis, it is found that the separatrix crossing behaviors is the dynamical mechanism behind measure synchronization transition in both time-discrete and time-continuous coupled Hamiltonian systems.
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Keywords:
- measure synchronization /
- Poincaré section /
- Hamiltonian systems
[1] ［1］ Kocarev L, Parlitz U 1996 Phys. Rev. Lett. 76 1816
[2] ［2］Boccaletti S， Valladares D L 2000 Phys. Rev. E 62 7497
[3] ［3］Masoller C 2001 Phys. Rev. Lett. 86 2782
[4] ［4］Pikovsky A, Rosenblum M, Kurths J 2001 Synchronization: A Universal Concept in Nonlinear Sciences (Cambridge: Cambridge University Press) p45
[5] ［5］Zhang T X, Zheng Z G 2004 Acta Phys. Sin. 53 3287 (in Chinese) ［张廷宪、郑志刚 2004 53 3287］
[6] ［6］Kaneko K 1986 Physica D 23 436
[7] ［7］Pecora L M， Carroll T L 1990 Phys. Rev. Lett. 64 821
[8] ［8］Womelsdorf T, Schoffelen J M, Oostenveld R, Singer W, Desimone R, Engel A K, Fries P 2007 Science 316 1609
[9] ［9］Bao G, Narenmandula, Tubuxin, Eredencang 2007 Acta Phys. Sin. 56 1971 (in Chinese) ［包刚、那仁满都拉、图布心、额尔顿仓 2007 56 1971］
[10] ］Zheng Z G, Hu G, Zhou C S, Hu B B 2000 Acta Phys. Sin. 49 2320 (in Chinese) ［郑志刚、胡岗、周昌松、胡斑比 2000 49 2320］
[11] ］Ma T D, Zhang H G, Wang Z L 2007 Acta Phys. Sin. 56 3796 (in Chinese) ［马铁东、张化光、王智良 2007 56 23796］
[12] ］Wu Y X, Huang X, Gao J, Zheng Z G 2007 Acta Phys. Sin. 56 3803 (in Chinese) ［吴玉喜、黄霞、高建、郑志刚 2007 56 3803］
[13] ］Hampton A, Zanette D H 1999 Phys. Rev. Lett. 83 2179
[14] ］Zheng Z G 2004 Spatiotemporal Dynamics and Collective Behaviors in Coupled Nonlinear Systems (Beijing: Higher Education Press) p143 (in Chinese) ［郑志刚 2004 耦合非线性系统的时空动力学与合作行为 (北京： 高等教育出版社) 第143页］
[15] ］Wang X G, Zhan M, Lai C H, Hu G 2003 Phys. Rev. E 67 066215
[16] ］Wang X G, Zhang Y, Hu G 2002 Phys. Lett. A 298 383
[17] ］Vincent U E 2005 New J. Phys. 7 209
[18] ］Chen S Y, Xu H B, Wang G R, Chen S G 2004 Acta Phys. Sin. 53 4098 (in Chinese) ［陈绍英、许海波、王光瑞、陈式刚 2004 53 4098］
[19] ］Zanette D H, Mikhailov A S 1997 Phys. Lett. A 235 135
[20] ］Lichenberg A J, Lieberman M A 1983 Regular and Stochastic Motion (New York: Springer-Verlag) p55
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[1] ［1］ Kocarev L, Parlitz U 1996 Phys. Rev. Lett. 76 1816
[2] ［2］Boccaletti S， Valladares D L 2000 Phys. Rev. E 62 7497
[3] ［3］Masoller C 2001 Phys. Rev. Lett. 86 2782
[4] ［4］Pikovsky A, Rosenblum M, Kurths J 2001 Synchronization: A Universal Concept in Nonlinear Sciences (Cambridge: Cambridge University Press) p45
[5] ［5］Zhang T X, Zheng Z G 2004 Acta Phys. Sin. 53 3287 (in Chinese) ［张廷宪、郑志刚 2004 53 3287］
[6] ［6］Kaneko K 1986 Physica D 23 436
[7] ［7］Pecora L M， Carroll T L 1990 Phys. Rev. Lett. 64 821
[8] ［8］Womelsdorf T, Schoffelen J M, Oostenveld R, Singer W, Desimone R, Engel A K, Fries P 2007 Science 316 1609
[9] ［9］Bao G, Narenmandula, Tubuxin, Eredencang 2007 Acta Phys. Sin. 56 1971 (in Chinese) ［包刚、那仁满都拉、图布心、额尔顿仓 2007 56 1971］
[10] ］Zheng Z G, Hu G, Zhou C S, Hu B B 2000 Acta Phys. Sin. 49 2320 (in Chinese) ［郑志刚、胡岗、周昌松、胡斑比 2000 49 2320］
[11] ］Ma T D, Zhang H G, Wang Z L 2007 Acta Phys. Sin. 56 3796 (in Chinese) ［马铁东、张化光、王智良 2007 56 23796］
[12] ］Wu Y X, Huang X, Gao J, Zheng Z G 2007 Acta Phys. Sin. 56 3803 (in Chinese) ［吴玉喜、黄霞、高建、郑志刚 2007 56 3803］
[13] ］Hampton A, Zanette D H 1999 Phys. Rev. Lett. 83 2179
[14] ］Zheng Z G 2004 Spatiotemporal Dynamics and Collective Behaviors in Coupled Nonlinear Systems (Beijing: Higher Education Press) p143 (in Chinese) ［郑志刚 2004 耦合非线性系统的时空动力学与合作行为 (北京： 高等教育出版社) 第143页］
[15] ］Wang X G, Zhan M, Lai C H, Hu G 2003 Phys. Rev. E 67 066215
[16] ］Wang X G, Zhang Y, Hu G 2002 Phys. Lett. A 298 383
[17] ］Vincent U E 2005 New J. Phys. 7 209
[18] ］Chen S Y, Xu H B, Wang G R, Chen S G 2004 Acta Phys. Sin. 53 4098 (in Chinese) ［陈绍英、许海波、王光瑞、陈式刚 2004 53 4098］
[19] ］Zanette D H, Mikhailov A S 1997 Phys. Lett. A 235 135
[20] ］Lichenberg A J, Lieberman M A 1983 Regular and Stochastic Motion (New York: Springer-Verlag) p55
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