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The study of a novel amplitude spiral wave in complex Ginzburg-Landau equation system is performed. The competition results between amplitude spiral waves and phase spiral waves and spatiotemporal chaos can be divided into four kind of regimes: regimes I and Ⅲ, in which the space of amplitude spiral waves is invaded by phase spiral waves, regime Ⅱ, in which the amplitude spiral waves are stronger than phase spiral waves, and regime IV, in which we have various results due to the existence of spatiotemporal chaos. Analysing the frequencies of amplitude spirals, phase spirals and spatiotemporal chaos, we find that when the parameters of spiral wave system α1=-1.34 and β1=0.35, the spiral wave with higher frequency will have better stability and can invade into low-frequency pattern space. The competition results are influenced by frequency of real part of the system variable. Our frequency analyses accord well with the numerical observations.
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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] Yu L C, Ma J, Zhang G Y, Chen Y 2008 Chin. Phys. Lett. 25 2706
[4] Lee K J, Cox E C, Goldstein R E 1996 Phys. Rev. Lett. 76 1174
[5] Tian C H, Deng M Y 2013 Acta Phys. Sin. 62 190503 (in Chinese) [田昌海, 邓敏艺 2013 物理学报 62 190503]
[6] Yuan G Y, Zhang H, Wang G R 2013 Acta Phys. Sin. 62 160502 (in Chinese) [袁国勇, 张焕, 王光瑞 2013 物理学报 62 160502]
[7] Zhou Z W, Cheng X J, Tian H T, Tang G N 2012 Acta Phys. Sin. 61 210506 (in Chinese) [周振玮, 陈醒基, 田海涛, 唐国宁 2012 物理学报 61 210506]
[8] Dong L F, Bai Z G, He Y F 2012 Acta Phys. Sin. 61 120509 (in Chinese) [董丽芳, 白占国, 贺亚峰 2012 物理学报 61 120509]
[9] Yuan X P, Chen J X, Zhao Y H, Lou Q, Wang L L, Shen Q 2011 Chin. Phys. Lett. 28 100505
[10] Qian Y 2012 Chin. Phys. B 21 088201
[11] 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)]
[12] Zhan M, Kapral R 2005 Phys. Rev. E 72 046221
[13] Gan Z N, Ma J, Zhang G Y, Chen Y 2008 Acta Phys. Sin. 57 5400 (in Chinese) [甘正宁, 马军, 张国勇, 陈勇 2008 物理学报 57 5400]
[14] Xie L L, Gao J H 2010 Chin. Phys. B 19 060516
[15] 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 物理学报 60 080503]
[16] Zhong M, Tang G N 2010 Acta Phys. Sin. 59 1593 (in Chinese) [钟敏, 唐国宁 2010 物理学报 59 1593]
[17] Gao J H, Xie L L, Nie H C, Zhan M 2010 Chaos 20 043132
[18] Xie L L, Gao J Z, Xie W M, Gao J H 2011 Chin. Phys. B 20 110503
[19] Gao J H, Xie W M, Gao J Z, Yang H P, Ge Z C 2012 Acta Phys. Sin. 61 130506 (in Chinese) [高继华, 谢伟苗, 高加振, 杨海朋, 戈早川 2012 物理学报 61 130506]
[20] He X Y, Zhang H, Hu B, Cao Z J, Zheng B, Hu G 2007 New J. Phys. 9 66
[21] Zhabotinsky A M, Muller S C, Hess B 1990 Chem. Phys. Lett. 172 445
[22] Winston D, Arora M, Maselko J, Gaspar V, Showalter K 1991 Nature 351 132
[23] Hildebrand M, Cui J X, Mihaliuk E, Wang J C, Showalter K 2003 Phys. Rev. E 68 026205
[24] Yang L F, Epstein I R 2003 Phys. Rev. Lett. 90 178303
[25] Yang H J, Yang J Z 2007 Phys. Rev. E 76 016206
[26] Kuramoto Y 1984 Chemical Oscillations, Waves, and Turbulence (New York: Springer)
[27] Cross M, Hohenberg P 1993 Rev. Mod. Phys. 65 851
[28] Aranson I S, Kramer L 2002 Rev. Mod. Phys. 74 99
[29] Das S K, Puri S, Cross M 2001 Phys. Rev. E 64 046206
[30] Ipsen M, van Hecke M 2001 Physica D 160 103
[31] van Hecke M 2003 Physica D 174 134
[32] Nie H C, Xie L L, Gao J H, Zhan M 2011 Chaos 21 023107
[33] Nie H C, Gao J H, Zhan M 2011 Phys. Rev. E 84 056204
[34] Zhan M, Wang X G, Gong X F, Lai C H 2005 Phys. Rev. E 71 036212
[35] Cui X H, Huang X Q, Xie F G, Hu G 2013 Phys. Rev. E 88 022905
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[1] Zaikin A N, Zhabotinsky A M 1970 Nature 225 535
[2] Masajada J, Dubik B 2001 Opt. Commun. 198 21
[3] Yu L C, Ma J, Zhang G Y, Chen Y 2008 Chin. Phys. Lett. 25 2706
[4] Lee K J, Cox E C, Goldstein R E 1996 Phys. Rev. Lett. 76 1174
[5] Tian C H, Deng M Y 2013 Acta Phys. Sin. 62 190503 (in Chinese) [田昌海, 邓敏艺 2013 物理学报 62 190503]
[6] Yuan G Y, Zhang H, Wang G R 2013 Acta Phys. Sin. 62 160502 (in Chinese) [袁国勇, 张焕, 王光瑞 2013 物理学报 62 160502]
[7] Zhou Z W, Cheng X J, Tian H T, Tang G N 2012 Acta Phys. Sin. 61 210506 (in Chinese) [周振玮, 陈醒基, 田海涛, 唐国宁 2012 物理学报 61 210506]
[8] Dong L F, Bai Z G, He Y F 2012 Acta Phys. Sin. 61 120509 (in Chinese) [董丽芳, 白占国, 贺亚峰 2012 物理学报 61 120509]
[9] Yuan X P, Chen J X, Zhao Y H, Lou Q, Wang L L, Shen Q 2011 Chin. Phys. Lett. 28 100505
[10] Qian Y 2012 Chin. Phys. B 21 088201
[11] 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)]
[12] Zhan M, Kapral R 2005 Phys. Rev. E 72 046221
[13] Gan Z N, Ma J, Zhang G Y, Chen Y 2008 Acta Phys. Sin. 57 5400 (in Chinese) [甘正宁, 马军, 张国勇, 陈勇 2008 物理学报 57 5400]
[14] Xie L L, Gao J H 2010 Chin. Phys. B 19 060516
[15] 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 物理学报 60 080503]
[16] Zhong M, Tang G N 2010 Acta Phys. Sin. 59 1593 (in Chinese) [钟敏, 唐国宁 2010 物理学报 59 1593]
[17] Gao J H, Xie L L, Nie H C, Zhan M 2010 Chaos 20 043132
[18] Xie L L, Gao J Z, Xie W M, Gao J H 2011 Chin. Phys. B 20 110503
[19] Gao J H, Xie W M, Gao J Z, Yang H P, Ge Z C 2012 Acta Phys. Sin. 61 130506 (in Chinese) [高继华, 谢伟苗, 高加振, 杨海朋, 戈早川 2012 物理学报 61 130506]
[20] He X Y, Zhang H, Hu B, Cao Z J, Zheng B, Hu G 2007 New J. Phys. 9 66
[21] Zhabotinsky A M, Muller S C, Hess B 1990 Chem. Phys. Lett. 172 445
[22] Winston D, Arora M, Maselko J, Gaspar V, Showalter K 1991 Nature 351 132
[23] Hildebrand M, Cui J X, Mihaliuk E, Wang J C, Showalter K 2003 Phys. Rev. E 68 026205
[24] Yang L F, Epstein I R 2003 Phys. Rev. Lett. 90 178303
[25] Yang H J, Yang J Z 2007 Phys. Rev. E 76 016206
[26] Kuramoto Y 1984 Chemical Oscillations, Waves, and Turbulence (New York: Springer)
[27] Cross M, Hohenberg P 1993 Rev. Mod. Phys. 65 851
[28] Aranson I S, Kramer L 2002 Rev. Mod. Phys. 74 99
[29] Das S K, Puri S, Cross M 2001 Phys. Rev. E 64 046206
[30] Ipsen M, van Hecke M 2001 Physica D 160 103
[31] van Hecke M 2003 Physica D 174 134
[32] Nie H C, Xie L L, Gao J H, Zhan M 2011 Chaos 21 023107
[33] Nie H C, Gao J H, Zhan M 2011 Phys. Rev. E 84 056204
[34] Zhan M, Wang X G, Gong X F, Lai C H 2005 Phys. Rev. E 71 036212
[35] Cui X H, Huang X Q, Xie F G, Hu G 2013 Phys. Rev. E 88 022905
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