多可激性障碍下的螺旋波动力学

袁国勇; 张焕; 王光瑞

doi:10.7498/aps.62.160502

摘要

在许多实际可激系统中局部不均匀是广泛存在的, 它们是螺旋波形成以及动力学行为改变的重要因素. 本文研究了可激性障碍对螺旋波动力学行为的影响. 研究表明, 在障碍区域内可激性参数大于区域外情况下障碍会对其附近的螺旋波波头有吸引作用, 多局部障碍共存时吸引行为不仅依赖障碍分布, 而且依赖障碍的大小以及区域内可激性参数的具体取值. 通过抑制变量小值区域的变化分析了这些行为发生的原因. 在障碍区域内可激性参数小于区域外情况下障碍对其近邻的螺旋波波头有排斥作用, 排斥后波头的运动依赖初始螺旋波是刚性旋转的还是漫游的. 多局部障碍共存时排斥作用对螺旋波动力学行为的改变依赖障碍的分布、大小与区域内可激性参数的具体取值以及初始螺旋波的类型.

关键词:

Abstract

Many real excitable systems can be descibed as inhomogeneous media, where the inhomogeneity is an important factor for the formation of spiral waves and the changing of their dynamics. In this paper, we investigate the effect of excitability obstacles on spiral-wave dynamics. For an excitability-reduced obstacle, the neighbor spiral tip is attracted into the obstacle. When more localized obstacles are placed, the attactive case depends on the distribution, size and excitability of the obstcales. On the basis of analyzing the small-value area of the inhibitor variable, we illustrate the mechanism of these behaviors occuring. For an excitability-enhanced obstacle, the nearby spiral tip is repelled. The tip motion after the repelsive effect depends on the type of the initial spiral wave, i.e. rigidily rotating spiral wave or meandering spiral wave. In the present of more localized obstacles, there exist different behaviors for different distributions, sizes and excitabilities of the obstcales, and different types of initial waves.

Keywords:

作者及机构信息

1.
河北师范大学物理科学与信息工程学院, 石家庄 050024;

2.
河北省新型薄膜材料实验室, 石家庄 050024;

3.
北京应用物理与计算数学研究所, 北京 100088

基金项目: 国家自然科学基金青年科学基金(批准号: 11005030);河北省自然科学基金(批准号: A2013205147)和河北省教育厅科研基金(批准号: 2009135)资助的课题.

Authors and contacts

1.
Department of Physics, Hebei Normal University, Shijiazhuang 050024, China;

2.
Hebei Advanced Thin Films Laboratory, Shijiazhuang 050024, China;

3.
Institute of Applied Physics and Computational Mathematics, Beijing 100088, China

Funds: Project supported by the Young Scientists Fund of the National Natural Science Foundation of China (Grant No. 11005030), the Natural Science Foundation of Hebei Province, China (Grant No. A2013205147), and the Scientific Research Fundation of the Education Department of Hebei Province, China (Grant No. 2009135).

参考文献

[1]	Cross M C, Hohenberg P C 1993 Rev. Mod. Phys. 65 851
[2]	Mikhailov A S, Showalter K 2006 Phys. Report 425 79
[3]	Frisch T, Rica S, Coullet P, Gilli J M 1994 Phys. Rev. Lett. 72 1471
[4]	Arecchi F T, Boccaletti S, Ramazza P 1999 Phys. Report 318 1
[5]	Van Oss C, Panfilov A V, Hogeweg P, Siegert F, Weijer C J 1996 J. Theor. Biol. 181 203
[6]	Lechleiter J, Girard S, Peralta E, Clapham D 1991 Science 252 123
[7]	Huang X Y, Xu W F, Liang J M, Takagaki K, Gao X, Wu J Y 2010 Neuron 68 978
[8]	Nettesheim S, Oertzen A V, Rotermund H H, Ertl G 1993 J. Chem. Phys. 98 9977
[9]	Dong L F, Wang H F, Liu F C, He Y F 2007 New. J. Phys. 9 330
[10]	Panfilov A V, Keener J P 1993 J. Theor. Biol. 163 439
[11]	Agladze K, Keener J P, Mller S C, Panfilov A 1994 Science 264 1746
[12]	Cabo C, Pertsov A M, Davidenko J M, Baxter W T, Gray R A, Jalife J 1996 Biophys. J. 70 1105
[13]	Fernández-García G, Gómez-Gesteira M, Muñuzuri A P, Pérez-Muñuzuri V, Pérez-Villar V 1994 Eur. J. Phys. 15 221
[14]	Cabo C, Pertsov A M, Baxter W T, Davidenko J M, Gray R A, Jalife J 1994 Circ. Res. 75 1014
[15]	Fast V G, Kléber A G. 1997 Cardiovasc. Res. 33 258
[16]	Xie F, Qu Z, Garfinkel A 1998 Phys. Rev. E 58 6355
[17]	Valderrábano M, Kim Y H, Yashima M, Wu T J, Karagueuzian H S, Chen P S 2000 J. Am. Coll. Cardiol. 36 2000
[18]	Shajahan T K, Sinha S, Pandit R 2007 Phys. Rev. E 75 011929
[19]	Shajahan T K, Nayak A R, Pandit R 2009 PLoS. ONE. 4 e4738
[20]	Zhang H, Ruan X S, Hu B B, Ouyang Q 2004 Phys. Rev. E 70 016212
[21]	Sridhar S, Sinha S, Panfilov A V 2010 Phys. Rev. E 82 051908
[22]	Xu L, Qu Z, Di Z 2009 Phys. Rev. E 79 036212
[23]	Wang P Y, Xie P 2000 Phys. Rev. E 61 5120
[24]	Wu N J, Zhang H, Ying H P, Cao Z J, Hu G 2006 Phys. Rev. E 73 060901R
[25]	Sakaguchi H, Fujimoto T 2003 Phys. Rev. E 67 067202
[26]	Ma J, Wang C N, Jin W Y, Li Y L, Pu Z S 2008 Chin. Phys. B 17 2844
[27]	Kim M, Bertram M, Pollmann M, von Oertzen A, Mikhailov A S, Rotermund H H, Ertl G 2001 Science 292 1357
[28]	Yuan G Y, Chen S G, Yang S P 2007 Eur. Phys. J. B 58 331
[29]	Agladze K, Kay M W, Krinsky V, Sarvazyan N 2007 Am. J. Physiol. Heart. Circ. Physiol. 293 H503
[30]	Zhang H, Cao Z, Wu N J, Ying H P, Hu G 2005 Phys. Rev. Lett. 94 188301
[31]	Tang G N, Deng M Y, Hu B, Hu G 2008 Phys. Rev. E 77 046217
[32]	Gottwald G, Pumir A, Krinsky V 2001 Chaos 11 487
[33]	Yuan G Y, Wang G R, Chen S G 2005 Europhys. Lett. 72 908
[34]	Ma J, Pu Z S, Feng W J, Li W X 2005 Acta. Phys. Sin. 54 4602 (in Chinese) [马军, 蒲忠胜, 冯旺军, 李维学 2005 54 4602]
[35]	Tanaka M, Isomura A, Hörning M, Kitahata H, Agladze K, Yoshikawa K 2009 Chaos 19 043114
[36]	Isomura A, Hörning M, Agladze K, Yoshikawa K 2008 Phys. Rev. E 78 066216
[37]	Hörning M, Isomura A, Agladze K, Yoshikawa K 2009 Phys. Rev. E 79 026218
[38]	Cherubini C, Filippi S, Gizzi A 2012 Phys. Rev. E 85 031915
[39]	Ávalos E, Lai P Y, Chan C K 2011 Europhys. Lett. 94 60006
[40]	Cysyk J, Tung L 2008 Biophys. J. 94 1533
[41]	Bittihn P, Squires A, Luther G, Bodenschatz E, Krinsky V, Parlitz U, Luther S 2010 Philos. Transact. A: Math. Phys. Eng. Sci. 368 2221

施引文献

[1]	Cross M C, Hohenberg P C 1993 Rev. Mod. Phys. 65 851
[2]	Mikhailov A S, Showalter K 2006 Phys. Report 425 79
[3]	Frisch T, Rica S, Coullet P, Gilli J M 1994 Phys. Rev. Lett. 72 1471
[4]	Arecchi F T, Boccaletti S, Ramazza P 1999 Phys. Report 318 1
[5]	Van Oss C, Panfilov A V, Hogeweg P, Siegert F, Weijer C J 1996 J. Theor. Biol. 181 203
[6]	Lechleiter J, Girard S, Peralta E, Clapham D 1991 Science 252 123
[7]	Huang X Y, Xu W F, Liang J M, Takagaki K, Gao X, Wu J Y 2010 Neuron 68 978
[8]	Nettesheim S, Oertzen A V, Rotermund H H, Ertl G 1993 J. Chem. Phys. 98 9977
[9]	Dong L F, Wang H F, Liu F C, He Y F 2007 New. J. Phys. 9 330
[10]	Panfilov A V, Keener J P 1993 J. Theor. Biol. 163 439
[11]	Agladze K, Keener J P, Mller S C, Panfilov A 1994 Science 264 1746
[12]	Cabo C, Pertsov A M, Davidenko J M, Baxter W T, Gray R A, Jalife J 1996 Biophys. J. 70 1105
[13]	Fernández-García G, Gómez-Gesteira M, Muñuzuri A P, Pérez-Muñuzuri V, Pérez-Villar V 1994 Eur. J. Phys. 15 221
[14]	Cabo C, Pertsov A M, Baxter W T, Davidenko J M, Gray R A, Jalife J 1994 Circ. Res. 75 1014
[15]	Fast V G, Kléber A G. 1997 Cardiovasc. Res. 33 258
[16]	Xie F, Qu Z, Garfinkel A 1998 Phys. Rev. E 58 6355
[17]	Valderrábano M, Kim Y H, Yashima M, Wu T J, Karagueuzian H S, Chen P S 2000 J. Am. Coll. Cardiol. 36 2000
[18]	Shajahan T K, Sinha S, Pandit R 2007 Phys. Rev. E 75 011929
[19]	Shajahan T K, Nayak A R, Pandit R 2009 PLoS. ONE. 4 e4738
[20]	Zhang H, Ruan X S, Hu B B, Ouyang Q 2004 Phys. Rev. E 70 016212
[21]	Sridhar S, Sinha S, Panfilov A V 2010 Phys. Rev. E 82 051908
[22]	Xu L, Qu Z, Di Z 2009 Phys. Rev. E 79 036212
[23]	Wang P Y, Xie P 2000 Phys. Rev. E 61 5120
[24]	Wu N J, Zhang H, Ying H P, Cao Z J, Hu G 2006 Phys. Rev. E 73 060901R
[25]	Sakaguchi H, Fujimoto T 2003 Phys. Rev. E 67 067202
[26]	Ma J, Wang C N, Jin W Y, Li Y L, Pu Z S 2008 Chin. Phys. B 17 2844
[27]	Kim M, Bertram M, Pollmann M, von Oertzen A, Mikhailov A S, Rotermund H H, Ertl G 2001 Science 292 1357
[28]	Yuan G Y, Chen S G, Yang S P 2007 Eur. Phys. J. B 58 331
[29]	Agladze K, Kay M W, Krinsky V, Sarvazyan N 2007 Am. J. Physiol. Heart. Circ. Physiol. 293 H503
[30]	Zhang H, Cao Z, Wu N J, Ying H P, Hu G 2005 Phys. Rev. Lett. 94 188301
[31]	Tang G N, Deng M Y, Hu B, Hu G 2008 Phys. Rev. E 77 046217
[32]	Gottwald G, Pumir A, Krinsky V 2001 Chaos 11 487
[33]	Yuan G Y, Wang G R, Chen S G 2005 Europhys. Lett. 72 908
[34]	Ma J, Pu Z S, Feng W J, Li W X 2005 Acta. Phys. Sin. 54 4602 (in Chinese) [马军, 蒲忠胜, 冯旺军, 李维学 2005 54 4602]
[35]	Tanaka M, Isomura A, Hörning M, Kitahata H, Agladze K, Yoshikawa K 2009 Chaos 19 043114
[36]	Isomura A, Hörning M, Agladze K, Yoshikawa K 2008 Phys. Rev. E 78 066216
[37]	Hörning M, Isomura A, Agladze K, Yoshikawa K 2009 Phys. Rev. E 79 026218
[38]	Cherubini C, Filippi S, Gizzi A 2012 Phys. Rev. E 85 031915
[39]	Ávalos E, Lai P Y, Chan C K 2011 Europhys. Lett. 94 60006
[40]	Cysyk J, Tung L 2008 Biophys. J. 94 1533
[41]	Bittihn P, Squires A, Luther G, Bodenschatz E, Krinsky V, Parlitz U, Luther S 2010 Philos. Transact. A: Math. Phys. Eng. Sci. 368 2221

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