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以双层耦合复金兹堡-朗道(Ginzburg-Landau)方程系统为时空模型, 研究了其中的模螺旋波, 讨论了这种特殊波动现象的稳定条件和相关影响因素. 模螺旋波与该类时空系统中常见的相螺旋波相比, 其中心不存在缺陷点, 同时仅在其变量的振幅部分(而非相位部分) 表现为螺旋结构. 本文通过数值方法研究了耦合复金兹堡-朗道方程中产生模螺旋波所需要的初始和参数条件.研究表明, 当双层耦合系统的初始斑图之间的差距较大时, 才能够产生模螺旋波; 同时观察到系统在参数不匹配的条件下会发生相螺旋波向模螺旋波的转变.通过对同步函数的计算, 发现该转变过程具有非连续性.A novel amplitude spiral wave in coupled complex Ginzburg-Landau equation (CGLE) system is proposed. The stability conditions and the relevant factors are investigated via numerical simulations. On the tip of an amplitude spiral wave there exist no topological defect, which is different from the commonly observed phase spiral wave, and in its amplitude part (instead of phase part) there is a spiral structure. In this research, the stability of amplitude spiral wave is studied by considering the different initial patterns in the case of the system parameter mismatches.
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Keywords:
- spiral wave /
- complex Ginzburg-Landau equation /
- amplitude spiral wave
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[59] -
[1] Zaikin A N, Zhabotinsky A M 1970 Nature 225 535
[2] Masajada J, Dubik B 2001 Opt. Commun. 198 21
[3] [4] Yu L C, Ma J, Zhang G Y, Chen Y 2008 Chin. Phys. Lett. 25 2706
[5] [6] Lee K J, Cox E C, Goldstein R E 1996 Phys. Rev. Lett. 76 1174
[7] [8] Goryachev A, Chate H, Kapral R 1998 Phys. Rev. Lett. 80 873
[9] [10] Vanag V K, Epstein I R 2001 Science 294 835
[11] [12] [13] Zaritski R M, Pertsov A M 2002 Phys. Rev. E 66 066120
[14] Gong Y F, Christini D J 2003 Phys. Rev. Lett. 90 088302
[15] [16] Ouyang Q 2000 Pattern Formation in Reaction-Diffusion Systems (Shanghai: Shanghai Scientific and Technological Education Publishing House) (in Chinese) [欧阳颀 2000 反应扩散系统中的斑图动力学(上海: 上海科技教育出版社)]
[17] [18] [19] Zhan M, Kapral R 2005 Phys. Rev. E 72 046221
[20] [21] Gan Z N, Ma J, Zhang G Y, Chen Y 2008 Acta Phy. Sin. 57 5400 (in Chinese) [甘正宁, 马军, 张国勇, 陈勇 2008 57 5400]
[22] [23] Xie L L, Gao J H 2010 Chin. Phys. B 19 060515
[24] [25] Gao J Z, Xie L L, Xie W M, Gao J H 2011 Acta Phys. Sin. 60 080503 (in Chinese) [高加振, 谢玲玲, 谢伟苗, 高继华 2011 60 080503]
[26] [27] Zhong M, Tang G N 2010 Acta Phys. Sin. 59 1593 (in Chinese) [钟敏, 唐国宁 2010 59 1593]
[28] [29] Gao J H, Xie L L, Nie H C, Zhan M 2010 Chaos 20 043132
[30] Xie L L, Gao J Z, Xie W M, Gao J H 2011 Chin. Phys. B 20 110503
[31] [32] He X Y, Zhang H, Hu B, Cao Z J, Zheng B, Hu G 2007 New J. Phys. 9 66
[33] [34] [35] Zhabotinsky A M, Muller S C, Hess B 1990 Chem. Phys. Lett. 172 445
[36] Winston D, Arora M, Maselko J, Gaspar V, Showalter K 1991 Nature (London) 351 132
[37] [38] [39] Hildebrand M, Cui J X, Mihaliuk E, Wang J C, Showalter K 2003 Phys. Rev. E 68 026205
[40] Yang L F, Epstein I R 2003 Phys. Rev. Lett. 90 178303
[41] [42] Yang H J, Yang J Z 2007 Phys. Rev. E 76 016206
[43] [44] Kuramoto Y 1984 Chemical Oscillations, Waves, and Turbulence (New York: Springer)
[45] [46] Cross M, Hohenberg P 1993 Rev. Mod. Phys. 65 851
[47] [48] Aranson I S, Kramer L 2002 Rev. Mod. Phys. 74 99
[49] [50] Das S K, Puri S, Cross M 2001 Phys. Rev. E 64 046206
[51] [52] [53] Ipsen M, van Hecke M 2001 Physica D 160 103
[54] [55] van Hecke M 2003 Physica D 174 134
[56] Nie H C, Xie L L, Gao J H, Zhan M 2011 Chaos 21 023107
[57] [58] Nie H C, Gao J H, Zhan M 2011 Phys. Rev. E 84 056204
[59]
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