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本文采用Br-Eiswirth模型研究了两层可激发介质中螺旋波的动力学, 两层介质采用抑制和兴奋性非对称耦合. 数值模拟结果表明: 兴奋性非对称耦合可以促进两个不同频率的螺旋波锁频, 即使初始频率相差大, 两螺旋波也能实现锁频, 这种耦合使两个螺旋波具有最强的锁频能力; 当两层介质采用抑制性非对称耦合时, 只有当两个初始螺旋波的频率差比较小才能实现锁频, 而且比一般扩散耦合的锁频范围窄, 两螺旋波锁频能力达到最低水平; 当耦合强度和控制参数适当选取时, 抑制性和兴奋性非对称耦合既可以使其中一层介质维持螺旋波态, 使另一层介质中的螺旋波演化到静息态或低频靶波态, 也可以使两层介质中的螺旋波都漫游, 或都转变成靶波, 最后这两个靶波要么消失, 要么转变成平面波状的振荡斑图, 而且两层介质振荡是反相的, 此外在模拟中还观察到两螺旋波局部间歇锁频现象, 这些结果有助于人们理解在心脏系统中出现的复杂现象.The dynamics of spiral waves in the two-layer excitable media is studied by using the Br-Eiswirth model. The two media adopts the inhibitory and excitatory asymmetric couplings. Numerical results show that the excitatory asymmetric coupling can promote the frequency-locking of two spiral waves with different frequencies. The two spiral waves can achieve frequency-locking even if the frequency difference between them is large. The coupling causes the two spiral waves to have the strongest ability of frequency-locking; when the coupling between the two media is the inhibitory asymmetric coupling, the two spiral waves can achieve frequency-locking only when the frequency difference of the initial spiral waves is small. Furthermore, the range of frequency-locking is smaller than that of the general feedback coupling, and the frequency-locking ability of spiral waves reaches the minimum level. When the coupling strength and control parameters are chosen appropriately, the inhibitory and excitatory asymmetric coupling can keep the spiral wave unchanged in one medium and result in the transition from spiral wave to the resting state or target wave with low-frequency in the other. The coupling also induces the meandering of spiral waves or leads to the transition from two spiral waves to two target waves in the two-layer media. Finally the generated target waves either disappear or develop into the plane-wave-like oscillation patterns. Furthermore, the oscillation of the patterns is in antiphase. In addition, the locally intermittent frequency-locking of the two spiral waves is observed. These results can help understand the complicated phenomena occurring in the cardiac system.
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Keywords:
- spiral wave /
- excitable medium /
- asymmetric coupling /
- frequency-locking
[1] Zaikin A N, Zhabotinsky A M 1970 Nature 225 535
[2] Gray R A, Pertsov A M, Jalife J 1998 Nature 392 75
[3] Yang H J, Yang J Z 2007 Phys. Rev. E 76 016206
[4] Witkowski F X, Leon L J, Penkoske P A, Giles W R, Spanoll M L, Ditto W L, Winfree A T 1998 Nature 392 78
[5] Fenton F H, Cherry E M, Hastings H M, Evans S J 2002 Chaos 12 852
[6] Cherry E M, Fenton F H 2008 New Journal of Physics 10 125016
[7] Cui X H, Huang X Q 2014 Journal of Henan Normal University (Natural Science Edition) 42 32 (in Chinese) [崔晓华, 黄晓清 2014 河南师范大学学报(自然科学版) 42 32]
[8] Sridhar S, Sinha S, Panfilov A V 2010 Phys. Rev. E 82 051908
[9] Zhan M, Wang X G, Gong X F, Lai C H 2005 Phys. Rev. E 71 036212
[10] Nie H C, Gao J H, Zhan M 2011 Phys. Rev. E 84 056204
[11] Valdrrbano M, Lee M H, Ohara T, Lai A C, Fishbein M, Lin S F, Karagueuzian H S, Chen P S 2001 Circulation Research 88 839
[12] Kneller J, Zou R, Vigmond E J, Wang Z G, Leon L J, Nattel S 2002 Circulation Research 90 1037
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[15] Qain Y 2012 Acta Phys. Sin. 61 158202(in Chinese) [钱郁 2012 61 158202]
[16] Ma J, Wang C N, Jin W Y, Li Y L, Pu Z S 2008 Chin. Phys. B 17 2844
[17] Chen X J, Qiao C G, Wang L L, Zhou Z W, Tian T T, Tang G N 2013 Acta Phys. Sin. 62 128201(in Chinese) [陈醒基, 乔成功, 王利利, 周振玮, 田涛涛, 唐国宁 2013 62 128201]
[18] Zhou Z W, Chen X J, Tian T T, Tang G N 2012 Acta Phys. Sin. 61 210506(in Chinese) [周振玮, 陈醒基, 田涛涛, 唐国宁 2012 61 210506]
[19] Hooks D A, Trew M L, Caldwell B J, Sands G B, LeGrice I J, Smaill B H 2007 Circ Res. 101 e103
[20] Gaudesius G, Miragoli M, Thomas S P, Rohr S 2003 Circulation Research 93 421
[21] Zhan H Q, Xia L, Shou G F, Zang Y L, Liu F, Crozier S 2014 J. Zhejiang Univ-Sci. B (Biomed Biotechnol) 15 225
[22] Lewis T J, Rinzel J 2003 Journal of Computational Neuroscience 14 283
[23] Br M, Eiswirth M 1993 Phys. Rev. E 48 R1635
[24] Sharma A, Shrimali M D 2012 Phys. Rev. E 85 057204
[25] Davidenko J M, Pertsov A V, Salomonsz R, Baxter B, Jalife J 1992 Nature 355 349
[26] Wren C 1998 Heart 79 536
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[1] Zaikin A N, Zhabotinsky A M 1970 Nature 225 535
[2] Gray R A, Pertsov A M, Jalife J 1998 Nature 392 75
[3] Yang H J, Yang J Z 2007 Phys. Rev. E 76 016206
[4] Witkowski F X, Leon L J, Penkoske P A, Giles W R, Spanoll M L, Ditto W L, Winfree A T 1998 Nature 392 78
[5] Fenton F H, Cherry E M, Hastings H M, Evans S J 2002 Chaos 12 852
[6] Cherry E M, Fenton F H 2008 New Journal of Physics 10 125016
[7] Cui X H, Huang X Q 2014 Journal of Henan Normal University (Natural Science Edition) 42 32 (in Chinese) [崔晓华, 黄晓清 2014 河南师范大学学报(自然科学版) 42 32]
[8] Sridhar S, Sinha S, Panfilov A V 2010 Phys. Rev. E 82 051908
[9] Zhan M, Wang X G, Gong X F, Lai C H 2005 Phys. Rev. E 71 036212
[10] Nie H C, Gao J H, Zhan M 2011 Phys. Rev. E 84 056204
[11] Valdrrbano M, Lee M H, Ohara T, Lai A C, Fishbein M, Lin S F, Karagueuzian H S, Chen P S 2001 Circulation Research 88 839
[12] Kneller J, Zou R, Vigmond E J, Wang Z G, Leon L J, Nattel S 2002 Circulation Research 90 1037
[13] Seipel M, Schneider F W, Mnster A F 2001 Faraday Discuss. 120 395
[14] Zhang H, Chen J X, Li Y Q, Xu J R 2006 The Journal of Chemical Physics 125 204503
[15] Qain Y 2012 Acta Phys. Sin. 61 158202(in Chinese) [钱郁 2012 61 158202]
[16] Ma J, Wang C N, Jin W Y, Li Y L, Pu Z S 2008 Chin. Phys. B 17 2844
[17] Chen X J, Qiao C G, Wang L L, Zhou Z W, Tian T T, Tang G N 2013 Acta Phys. Sin. 62 128201(in Chinese) [陈醒基, 乔成功, 王利利, 周振玮, 田涛涛, 唐国宁 2013 62 128201]
[18] Zhou Z W, Chen X J, Tian T T, Tang G N 2012 Acta Phys. Sin. 61 210506(in Chinese) [周振玮, 陈醒基, 田涛涛, 唐国宁 2012 61 210506]
[19] Hooks D A, Trew M L, Caldwell B J, Sands G B, LeGrice I J, Smaill B H 2007 Circ Res. 101 e103
[20] Gaudesius G, Miragoli M, Thomas S P, Rohr S 2003 Circulation Research 93 421
[21] Zhan H Q, Xia L, Shou G F, Zang Y L, Liu F, Crozier S 2014 J. Zhejiang Univ-Sci. B (Biomed Biotechnol) 15 225
[22] Lewis T J, Rinzel J 2003 Journal of Computational Neuroscience 14 283
[23] Br M, Eiswirth M 1993 Phys. Rev. E 48 R1635
[24] Sharma A, Shrimali M D 2012 Phys. Rev. E 85 057204
[25] Davidenko J M, Pertsov A V, Salomonsz R, Baxter B, Jalife J 1992 Nature 355 349
[26] Wren C 1998 Heart 79 536
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