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Dynamic behaviors of sparse and dense spirals are investigated numerically based on a Barkley model in heterogeneous excitable media. It is found that the rotating frequency of sparse spiral wave decreases rapidly with b increasing and then tends to saturation, which is different from that of dense spiral wave. The period and wavelength of dense spiral wave increase with the increase of parameter or the size R of localized inhomogeneity, which depends more sensitively on the size R than those of sparse sprial wave. The change of the speed of dense spiral wave tip with R is opposite to that of the sparse spiral wave tip. In addition, inhomogeneous effect gives rise to a defect point in arm of each of the two spiral waves when or b increases above a critical value.
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Keywords:
- spiral waves /
- localized inhomogeneity /
- excitable media /
- dynamics behaviors
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[2] Arthur T Winfree A 1991 Chaos 1 303
[3] Barkley D 1994 Phys. Rev. Lett.72 164
[4] Barkley D 1992 Phys. Rev. Lett. 68 2090
[5] Ouyang Q 2000 Pattern Formation in Reaction-Diffusion Systems (Shanghai: Shanghai Scientific & Technological Education Publishing House) pp73--77 (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)第73---77页]
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[7] Ma J, Tang J 2011 Optimal Control for Patterns in Space-time System (Wuhan: Huazhong University of Science and Technology Publishing House) pp104--130 (in Chinese) [马军, 唐军 2011 时空系统斑图优化控制 (武汉:华中科技大学出版社)第104--130页]
[8] Ma J Zhang A H Tang J Jin W Y 2010 J. Bio. Sys. 18 243
[9] Ma J, Tang J, Zhang A H Jia Y 2010 Sci. China Phys. Mech. Astron. 53 672
[10] Ma J, Wu Y, Ying H P, Jia Y 2011 Chinese Sci. Bull. 56 151
[11] Wang Q Y, Matjaz P, Duan Z S, Chen G R 2008 Phys. Lett. A 372 5681
[12] Jimenez Z A, Marts B, Steinbock O 2009 Phys. Rev. Lett. 102 244101
[13] Shajahan T K, Nayak A R, Pandit R 2009 PLoS ONE 4 e4738
[14] Alberto P M, Vicente P M, Vicente P V 1998 Phys. Rev. E 58 R2689
[15] Lin Z Y, Maskara B, Aguel F, Emokpae R, Tung Jr L 2006 Circulation 114 2113
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[17] Sungjae W, Jinhee H, Tae Yu K, Byung W B, Kyoung J L 2008 New Journal of Physics 10 015005
[18] Zhang G Y, Ma J, Gan Z N, Chen Y 2008 Acta Phys. Sin. 57 6815 (in Chinese) [张国勇, 马军, 甘正宁, 陈勇 2008 57 6815]
[19] Dai Y Wei H M, Tang G N 2010 Acta Phys. Sin. 59 5979 (in Chinese) [戴瑜, 韦海明, 唐国宁 2010 59 5979]
[20] Wei H M, Tang G N 2011 Acta Phys. Sin. 60 040504 (in Chinese) [韦海明, 唐国宁 2011 60 040504]
[21] Fu Y Q, Zhang H, Cao Z J, Zheng B, Hu G 2005 Phys. Rev. E 72 046206
[22] Akihiro I, Marcel H, Konstantin A, Kenichi Y 2008 Phys. Rev. E 78 066216
[23] Yuan G Y, Yang S P, Wang G R, Chen S G 2008 Chin. Phys. Soc. 17 1925
[24] Joseph Tranquillo, Meghan Howes, 2008 Phys. Rev. E 78 051914
[25] Biktashev V N Barkley D, Biktasheva I V 2010 Phys. Rev. Lett. 104 058302
[26] Shajahan T K, Sitabhra S, Pandit R 2007 Phys. Rev. E 75 011929
[27] Nattel S 2002 Nature 415 219
[28] Marban E 2002 Nature 415 213
[29] Xu L D, Qu Z L, Di Z R 2009 Phys. Rev. E 79 036212
[30] Biktashev I V Barkley D, Biktashev V N, Bordyugov G V, Foulkes A J 2009 Phys. Rev. E 79 056702
[31] Barkley D 1991 Physica D 49 61
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[1] Zaikin A N, Zhabotinsky A M 1970 Nature 225 535
[2] Arthur T Winfree A 1991 Chaos 1 303
[3] Barkley D 1994 Phys. Rev. Lett.72 164
[4] Barkley D 1992 Phys. Rev. Lett. 68 2090
[5] Ouyang Q 2000 Pattern Formation in Reaction-Diffusion Systems (Shanghai: Shanghai Scientific & Technological Education Publishing House) pp73--77 (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)第73---77页]
[6] Krinsky V Hamm E Voignier V 1996 Phys. Rev. Lett. 76 3854
[7] Ma J, Tang J 2011 Optimal Control for Patterns in Space-time System (Wuhan: Huazhong University of Science and Technology Publishing House) pp104--130 (in Chinese) [马军, 唐军 2011 时空系统斑图优化控制 (武汉:华中科技大学出版社)第104--130页]
[8] Ma J Zhang A H Tang J Jin W Y 2010 J. Bio. Sys. 18 243
[9] Ma J, Tang J, Zhang A H Jia Y 2010 Sci. China Phys. Mech. Astron. 53 672
[10] Ma J, Wu Y, Ying H P, Jia Y 2011 Chinese Sci. Bull. 56 151
[11] Wang Q Y, Matjaz P, Duan Z S, Chen G R 2008 Phys. Lett. A 372 5681
[12] Jimenez Z A, Marts B, Steinbock O 2009 Phys. Rev. Lett. 102 244101
[13] Shajahan T K, Nayak A R, Pandit R 2009 PLoS ONE 4 e4738
[14] Alberto P M, Vicente P M, Vicente P V 1998 Phys. Rev. E 58 R2689
[15] Lin Z Y, Maskara B, Aguel F, Emokpae R, Tung Jr L 2006 Circulation 114 2113
[16] Pazo D, Kramer L, Pumir A, Kanani S, Efimov I, Krinsky V 2004 Phys. Rev. Lett. 93 168303
[17] Sungjae W, Jinhee H, Tae Yu K, Byung W B, Kyoung J L 2008 New Journal of Physics 10 015005
[18] Zhang G Y, Ma J, Gan Z N, Chen Y 2008 Acta Phys. Sin. 57 6815 (in Chinese) [张国勇, 马军, 甘正宁, 陈勇 2008 57 6815]
[19] Dai Y Wei H M, Tang G N 2010 Acta Phys. Sin. 59 5979 (in Chinese) [戴瑜, 韦海明, 唐国宁 2010 59 5979]
[20] Wei H M, Tang G N 2011 Acta Phys. Sin. 60 040504 (in Chinese) [韦海明, 唐国宁 2011 60 040504]
[21] Fu Y Q, Zhang H, Cao Z J, Zheng B, Hu G 2005 Phys. Rev. E 72 046206
[22] Akihiro I, Marcel H, Konstantin A, Kenichi Y 2008 Phys. Rev. E 78 066216
[23] Yuan G Y, Yang S P, Wang G R, Chen S G 2008 Chin. Phys. Soc. 17 1925
[24] Joseph Tranquillo, Meghan Howes, 2008 Phys. Rev. E 78 051914
[25] Biktashev V N Barkley D, Biktasheva I V 2010 Phys. Rev. Lett. 104 058302
[26] Shajahan T K, Sitabhra S, Pandit R 2007 Phys. Rev. E 75 011929
[27] Nattel S 2002 Nature 415 219
[28] Marban E 2002 Nature 415 213
[29] Xu L D, Qu Z L, Di Z R 2009 Phys. Rev. E 79 036212
[30] Biktashev I V Barkley D, Biktashev V N, Bordyugov G V, Foulkes A J 2009 Phys. Rev. E 79 056702
[31] Barkley D 1991 Physica D 49 61
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