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The effect of small heterogeneous grains with different features and shapes on the evolution of spiral wave is investigated by using the simple model of discrete excitable medium. When the small grains are uniformly distributed in a medium,the instability of spiral wave relates to the shape,density and nature of the grain. The numerical results show that under suitable conditions,the heterogeneous grains can lead to the transition from stable spiral wave to meandering spiral wave in the medium in which it occurs, the spiral wave even drifts out of the boundary of system. The periodic pattern with irregular shape and the periodic maze-type pattern have been observed for the first time. The physical mechanism underlying these phenomena is discussed.
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Keywords:
- cellular automaton /
- excitable medium /
- maze-type pattern
[1] Frisch T,Rica S,Coullet P,Gilli J M 1994 Phys. Rev. Lett. 72 1471
[2] Plapp B B,Egolf D A,Bodenschatz E,Pesch W 1998 Phys. Rev. Lett. 81 5334
[3] Jakubith S,Rotermund H H,Engel W,Von Oertzen A,Ertl G 1990 Phys. Rev. Lett. 65 3013
[4] Agladze K I,De Kepper P 1992 J. Phys. Chem. 96 5239
[5] Witkowski F X,Leon J L,Penkoske P A,Giles W R,Spanok M L,Ditto W L,Winfree A T 1998 Nature 392 78
[6] Yin X,Liu Y 2008 Acta Phys. Sin. 57 6844 (in chinese) [尹小舟、刘 勇 2008 物理学报 57 6844]
[7] 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 物理学报 57 2832]
[8] 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 物理学报 57 2832]
[9] Ma J,Wang C N,Jin W Y,Li Y L,Pu Z S 2008 Chin. Phys. B 17 2844
[10] Gan Z N,Ma J,Zhang G Y,Chen Y 2008 Chin. Phys. B 17 4047
[11] Yang J Z,Zhang M 2005 Chin. Phys. Lett. 22 3195
[12] Br M,Bangia A K,Kevrekidis I G,Haas G,Rotermund H H,Ertl G 1996 J. Phys. Chem. 100 19106
[13] Zou X,Levine H,Kessler D A 1993 Phys. Rev. E 47 R800
[14] Pazó D,Kramer L,Pumir A,Kanani S,Efimov I,Krinsky V 2004 Phys. Rev. Lett. 93 168303
[15] Tusscher K H W J,Panfilov A V 2003 Phys. Rev. E 68 62902
[16] Xie F,Qu Z,Weiss J N,Garfinkel G 2001 Phys. Rev. E 63 31905
[17] De Bakker J M,van Capelle F J,Janse M J,Wilde A A,Coronel R,Becker A E,Dingemans K P,van Hemel N M,Hauer R N 1998 Circulation 77 589
[18] Panfilov A V 1998 Chaos 8 57
[19] Greenberg J M,Hastings S P 1978 SIAM Journal on Applied Mathematics 34 515
[20] Dai Y,Tang G N 2009 Acta Phys. Sin. 58 3 (in Chinese) [戴 瑜、唐国宁 2009 物理学报 58 3]
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[1] Frisch T,Rica S,Coullet P,Gilli J M 1994 Phys. Rev. Lett. 72 1471
[2] Plapp B B,Egolf D A,Bodenschatz E,Pesch W 1998 Phys. Rev. Lett. 81 5334
[3] Jakubith S,Rotermund H H,Engel W,Von Oertzen A,Ertl G 1990 Phys. Rev. Lett. 65 3013
[4] Agladze K I,De Kepper P 1992 J. Phys. Chem. 96 5239
[5] Witkowski F X,Leon J L,Penkoske P A,Giles W R,Spanok M L,Ditto W L,Winfree A T 1998 Nature 392 78
[6] Yin X,Liu Y 2008 Acta Phys. Sin. 57 6844 (in chinese) [尹小舟、刘 勇 2008 物理学报 57 6844]
[7] 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 物理学报 57 2832]
[8] 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 物理学报 57 2832]
[9] Ma J,Wang C N,Jin W Y,Li Y L,Pu Z S 2008 Chin. Phys. B 17 2844
[10] Gan Z N,Ma J,Zhang G Y,Chen Y 2008 Chin. Phys. B 17 4047
[11] Yang J Z,Zhang M 2005 Chin. Phys. Lett. 22 3195
[12] Br M,Bangia A K,Kevrekidis I G,Haas G,Rotermund H H,Ertl G 1996 J. Phys. Chem. 100 19106
[13] Zou X,Levine H,Kessler D A 1993 Phys. Rev. E 47 R800
[14] Pazó D,Kramer L,Pumir A,Kanani S,Efimov I,Krinsky V 2004 Phys. Rev. Lett. 93 168303
[15] Tusscher K H W J,Panfilov A V 2003 Phys. Rev. E 68 62902
[16] Xie F,Qu Z,Weiss J N,Garfinkel G 2001 Phys. Rev. E 63 31905
[17] De Bakker J M,van Capelle F J,Janse M J,Wilde A A,Coronel R,Becker A E,Dingemans K P,van Hemel N M,Hauer R N 1998 Circulation 77 589
[18] Panfilov A V 1998 Chaos 8 57
[19] Greenberg J M,Hastings S P 1978 SIAM Journal on Applied Mathematics 34 515
[20] Dai Y,Tang G N 2009 Acta Phys. Sin. 58 3 (in Chinese) [戴 瑜、唐国宁 2009 物理学报 58 3]
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