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采用 Bär 模型研究了通过被动介质耦合的两二维可激发系统中螺旋波的同步, 被动介质由可激发元素组成, 这些元素之间不存在耦合. 数值模拟结果表明, 被动介质对螺旋波的同步有很大影响, 当两系统中的初态螺旋波相同时, 被动介质可导致稳定螺旋波发生漫游, 螺旋波转变为螺旋波对或反靶波; 当两系统中的初态螺旋波不同步时, 在适当的参数下, 两螺旋波可以实现同步、相同步, 此外还观察到两螺旋波波头相互排斥、多螺旋波共存、同步的时空周期斑图、 系统演化到静息态等现象. 在被动介质中, 一般可观察到波斑图, 但是在某些情况下, 被动介质会出现同步振荡现象. 这些结果有助于人们理解心脏系统中出现的时空斑图.Synchronization of two spiral waves in two-dimensional excitable systems interacting through a passive medium is studied by using the Bär model. The passive medium is composed of excitable elements. There are no couplings among these elements. The numerical results show that synchronization of spiral waves is significantly affected by the passive medium. When two subsystems have the same initial spiral waves, the passive medium can induce meander of stable spiral waves and cause spiral waves to transform into multi-spiral waves or anti-target waves. When initial spiral waves are in an asynchronization state, the synchronization and phase-synchronization between two spiral waves are established if the relevant parameters are properly chosen. In addition, the following phenomena are observed: the tips of two spiral waves repel each other, multi-spiral waves coexist, synchronized spatiotemporal pattern repeats periodically, and the two systems evolves into the resting state. Wave patterns can generally be observed in passive medium. However, passive medium can exhibit synchronous oscillation in certain circumstances. These results can help one understand the formation of spatiotemporal patterns in the cardiac system.
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Keywords:
- spiral wave /
- coupling /
- synchronization /
- passive medium
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[15] Hildebrand M, Cui J X, Mihaliuk E, Wang J C, Showalter K 2003 Phys. Rev. E 68 026205
[16] Qian Y, Song X Y, Shi W, Chen G Z, Xue Y 2006 Acta Phys. Sin. 55 4420 (in Chinese) [钱郁, 宋宣玉, 时伟, 陈光旨, 薛郁 2006 55 4420]
[17] Nie H C, Xie L L, Gao J H, Zhan M 2011 Chaos 21 023107
[18] Yuan G Y, Yang S P, Wang G R, Chen S G 2005 Acta Phys. Sin. 54 1510 (in Chinese) [袁国勇, 杨世平, 王光瑞, 陈式刚 2005 54 1510]
[19] Gao J Z, Yang S X, Xie L L, Gao J H 2011 Chin. Phys. B 20 030505
[20] Li G Z, Chen Y Q, Tang G N 2012 Acta Phys. Sin. 61 020502 (in Chinese) [黎广钊, 陈永淇, 唐国宁 2012 61 020502]
[21] Bär M, Eiswirth M 1993 Phys. Rev. E 48 R1635
[22] Miragoli M, Gaudesius G, Rohr S 2006 Circ. Res. 98 801
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[1] Lechleiter J, Girard S, Peralta E, Clapham D 1991 Science 252 123
[2] Gray R A, Pertsov A M, Jalife J 1998 Nature 392 75
[3] Witkowski F X, Leon L J, Penkoske P A, Giles W R, Spano M L, Ditto W L, Winfree A T 1998 Nature 392 78
[4] Zaikin A N, Zhabotinsky A M 1970 Nature 225 535
[5] Bär M, Gottschalk N, Ertl G 1994 J. Phys. Chem. B 100 1202
[6] Harris-White M E, Zanotti S A, Frautschy S A, Charles A C 1998 J. Neurophysiol. 79 1045
[7] Wilkins M, Sneyd J 1998 J. Theor. Biol. 191 299
[8] Deng M Y, Tang G N, Kong L J, Liu M R 2010 Acta Phys. Sin. 59 2339 (in Chinese) [邓敏艺, 唐国宁, 孔令江, 刘慕仁 2010 59 2339]
[9] Tang D N, Tang G N 2010 Acta Phys. Sin. 59 2319 (in Chinese) [唐冬妮, 唐国宁 2010 59 2319]
[10] Antzelevitch C 2001 Cardiovasc. Res. 50 426
[11] Petrov V S, Osipov G V, Kurths J 2010 Phys. Rev. E 82 026208
[12] Miragoli M, Salvarini N, Rohr S 2007 Circ. Res. 101 755
[13] Li G Z, Chen Y Q, Tang G N, Liu J X 2011 Chin. Phys. Lett. 28 020504
[14] Nie H C, Gao J H, Zhan M 2011 Phys. Rev. E 84 056204
[15] Hildebrand M, Cui J X, Mihaliuk E, Wang J C, Showalter K 2003 Phys. Rev. E 68 026205
[16] Qian Y, Song X Y, Shi W, Chen G Z, Xue Y 2006 Acta Phys. Sin. 55 4420 (in Chinese) [钱郁, 宋宣玉, 时伟, 陈光旨, 薛郁 2006 55 4420]
[17] Nie H C, Xie L L, Gao J H, Zhan M 2011 Chaos 21 023107
[18] Yuan G Y, Yang S P, Wang G R, Chen S G 2005 Acta Phys. Sin. 54 1510 (in Chinese) [袁国勇, 杨世平, 王光瑞, 陈式刚 2005 54 1510]
[19] Gao J Z, Yang S X, Xie L L, Gao J H 2011 Chin. Phys. B 20 030505
[20] Li G Z, Chen Y Q, Tang G N 2012 Acta Phys. Sin. 61 020502 (in Chinese) [黎广钊, 陈永淇, 唐国宁 2012 61 020502]
[21] Bär M, Eiswirth M 1993 Phys. Rev. E 48 R1635
[22] Miragoli M, Gaudesius G, Rohr S 2006 Circ. Res. 98 801
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