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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
[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] -
[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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