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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.
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Keywords:
- spiral wave /
- spatiotemporal chaos /
- excitability obstacle
[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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[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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