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The alternans behavior is considered in the Greenberg-Hasting model of discrete excitable medium. The effect of the alternans behavior on spiral wave is investigated. The numerical results show that when the relevant parameters are appropriately chosen the alternans behavior has a significant influence on spiral waves. For example, the alternans behavior leads to the oscillation of the shape of the spiral wave and to the generation of the breathing spiral wave. The alternans behavior induces the meandering and the drifting of spiral waves, even causes spiral wave to move out of the system. Spiral wave can break up into multiple spiral waves, anti-target wave and spatiotemporal chaos due to the alternans behavior. The phenomena that the alternans behavior leads to the conduction barrier in homogeneous medium and causes spiral wave to break up or vanish, are observed for the first time. The physical mechanisms about these phenomena are briefly analyzed.
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Keywords:
- discrete excitable medium /
- spiral wave /
- target wave /
- meandering
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[2] Cross M C, Hohenberg P C 1993 Rev. Mod. Phys. 65 851
[3] Glass L 1996 Physics Today 8 40
[4] Ouyang Q 2001 Physics. 30 30 (in Chinese) [欧阳颀 2001 物理 30 30]
[5] Qu Z L, Xie F G, Garfinkel A A, James N W 2000 Annals of Biomedical Engineering 28 755
[6] Qian Y, Song X Y, Shi W 2006 Acta Phys. Sin. 55 4420 (in Chinese) [钱 郁 、宋宣玉、时 伟 2006 55 4420]
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[11] Ma J, Ying H P, Liu Y, Li S R 2009 Chin. Phys. B 18 98
[12] Deng M Y,Tang G N,Kong L J, Liu M R 2010 Chin. Phys. B 19 2339
[13] Ma J,Yi M, Li B W, Li Y L 2008 Chin. Phys. B 17 2438
[14] Ma J,Jin W Y,Li Y L,Zheng Y 2007 Acta Phys. Sin. 56 2456 (in Chinese) [马 军、靳伍银、李延龙、陈 勇 2007 物理学 报 56 2456] 〖15] Br M, Eiswirth M 1993 Phys. Rev. E 48 1635
[15] Dai Y, Tang G N 2009 Acta Phys. Sin. 58 3 (in Chinese) [戴 瑜、唐国宁 2009 58 3]
[16] Wang S H, Choe W G, Lee K J 2000 Phys. Rev. E 62 4799
[17] Tang D N, Tang G N 2010 Acta Phys. Sin. 59 2319 (in Chinese) [唐冬妮、唐国宁 2010 59 2319]
[18] 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 57 5400]
[19] Ma J, Jin W Y, Yi M, Li Y L 2008 Acta Phys. Sin. 57 2832 (in Chinese) [马 军、靳伍银、易 鸣、李延龙 2008 57 2832]
[20] Ma J,Wang C N, Jin W Y, Li Y L, Pu Z S 2008 Chin. Phys. B 17 2844
[21] Yang J Z, Zhang M 2005 Chin. Phys. Lett. 22 3195
[22] Kurz R W, Mohabir R, Ren Z L,Franzt M R 1993 European Heart Journal 14 1410
[23] Dilly S G, Lab M J 1988 Journal of Physiology 402 315
[24] Greenberg J M, Hastings S P 1978 SIAM Journal on Applied Mathematics 34 515
[25] Zhong M, Tang G N 2010 Acta Phys. Sin. 59 3070 (in Chinese) [钟 敏、唐国宁 2010 59 3070]
[26] Qu Z, Xie F, Garfinkel A, Weiss J N 2000 Annals of Biomedical Engineering 28 755
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[1] Zaikin A N, Zhabotinsky A M 1970 Nature 225 535
[2] Cross M C, Hohenberg P C 1993 Rev. Mod. Phys. 65 851
[3] Glass L 1996 Physics Today 8 40
[4] Ouyang Q 2001 Physics. 30 30 (in Chinese) [欧阳颀 2001 物理 30 30]
[5] Qu Z L, Xie F G, Garfinkel A A, James N W 2000 Annals of Biomedical Engineering 28 755
[6] Qian Y, Song X Y, Shi W 2006 Acta Phys. Sin. 55 4420 (in Chinese) [钱 郁 、宋宣玉、时 伟 2006 55 4420]
[7] Liu F C, Wang X F, Li X C, Dong L F 2007 Chin. Phys. 16 2640
[8] Yin X, Liu Y 2008 Acta Phys. Sin. 57 6844 (in Chinese) [尹小舟、刘 勇 2008 57 6844]
[9] Ma J, Jin W Y, Yi M, Li Y L 2008 Acta Phys. Sin. 57 2832 (in Chinese) [马 军、靳伍银、易 鸣、李延龙 2008 57 2832]
[10] Zhang G Y, Ma J, Gan Z N, Chen Y 2008 Acta Phys. Sin. 57 6815 (in Chinese) [张国用、马 军、甘正宁、陈 勇 2008 57 2832]
[11] Ma J, Ying H P, Liu Y, Li S R 2009 Chin. Phys. B 18 98
[12] Deng M Y,Tang G N,Kong L J, Liu M R 2010 Chin. Phys. B 19 2339
[13] Ma J,Yi M, Li B W, Li Y L 2008 Chin. Phys. B 17 2438
[14] Ma J,Jin W Y,Li Y L,Zheng Y 2007 Acta Phys. Sin. 56 2456 (in Chinese) [马 军、靳伍银、李延龙、陈 勇 2007 物理学 报 56 2456] 〖15] Br M, Eiswirth M 1993 Phys. Rev. E 48 1635
[15] Dai Y, Tang G N 2009 Acta Phys. Sin. 58 3 (in Chinese) [戴 瑜、唐国宁 2009 58 3]
[16] Wang S H, Choe W G, Lee K J 2000 Phys. Rev. E 62 4799
[17] Tang D N, Tang G N 2010 Acta Phys. Sin. 59 2319 (in Chinese) [唐冬妮、唐国宁 2010 59 2319]
[18] 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 57 5400]
[19] Ma J, Jin W Y, Yi M, Li Y L 2008 Acta Phys. Sin. 57 2832 (in Chinese) [马 军、靳伍银、易 鸣、李延龙 2008 57 2832]
[20] Ma J,Wang C N, Jin W Y, Li Y L, Pu Z S 2008 Chin. Phys. B 17 2844
[21] Yang J Z, Zhang M 2005 Chin. Phys. Lett. 22 3195
[22] Kurz R W, Mohabir R, Ren Z L,Franzt M R 1993 European Heart Journal 14 1410
[23] Dilly S G, Lab M J 1988 Journal of Physiology 402 315
[24] Greenberg J M, Hastings S P 1978 SIAM Journal on Applied Mathematics 34 515
[25] Zhong M, Tang G N 2010 Acta Phys. Sin. 59 3070 (in Chinese) [钟 敏、唐国宁 2010 59 3070]
[26] Qu Z, Xie F, Garfinkel A, Weiss J N 2000 Annals of Biomedical Engineering 28 755
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