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The numerical study on the effect of the earlyafterdepolarization on spiral wavesin discrete excitable media

Wei Hai-Ming Tang Guo-Ning

The numerical study on the effect of the earlyafterdepolarization on spiral wavesin discrete excitable media

Wei Hai-Ming, Tang Guo-Ning
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  • The early afterdepolarization (EAP) behavior is introduced into the Greeberg-Hasting model of discrete excitable medium through considering that some of the refractory states can be excited. The effect of the EAP on spiral wave is studied. The numerical results show that the EAP has significant influences on spiral waves when the related parameters are suitably chosen. These influences include that the EAP causes spiral wave drifting and meandering,and spiral breakup. The pattern of spiral wave is distorted. The spiral wave varies alternately between those with thick and thin arms. The period of spiral wave alters alternately between two values. The EAP induces the transition from stable spiral wave to breathing spiral wave or antispiral wave. When the excitation threshold of refractory states is very high,the EAP has no affect on the spiral wave. The EAP induced phenomena are briefly discussed.
    • Funds:
    [1]

    Fenton F H, Cherry E M, Hasting H M 2002 Chaos 12 852

    [2]

    Cross M C, Hohenberg P C 1993 Rev. Mod. Phys. 65 851

    [3]

    Zaikin A N, Zhabotinsky A M 1970 Nature 225 535

    [4]

    Br M, Kevrekidis I G, Rotermund H H, Ertl G 1995 Phys. Rev. E 52 R5739

    [5]

    Lee K J, Cox E C, Goldstein R E 1996 Phys. Rev. Lett. 76 1174

    [6]

    Qian Y, Song X Y, Shi W 2006 Acta Phys. Sin. 55 4420 (in chinese) [钱 郁 、宋宣玉、时 伟 2006 物理学报 55 4420]

    [7]

    Liu Fu 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 物理学报 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 物理学报 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 物理学报 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]

    Br M, Eiswirth M 1993 Phys. Rev. E 48 1635

    [16]

    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]

    [17]

    Wang S H, Choe W G, Lee K J 2000 Phys. Rev. E 62 4799

    [18]

    Tang D N, Tang G N 2010 Acta Phys. Sin. 59 2319 (in Chinese) [唐冬妮、唐国宁 2010物理学报 59 2319]

    [19]

    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 物理学报 57 5400]

    [20]

    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]

    [21]

    Ma J, Wang C N, Jin W Y, Li Y L, Pu Z S 2008 Chin. Phys. B 17 2844

    [22]

    Yang J Z, Zhang M 2005 Chin. Phys. Lett. 22 3195

    [23]

    Gerhardt M, Schuster H, Tyson J J 1990 Physica D 46 392

    [24]

    Weimar J R, Tyson J J, Watson L T 1992 Physica D 55 309

    [25]

    Greenberg J M, Hastings S P 1978 SIAM Journal on Applied Mathematics 34 515

    [26]

    Qu Z, Xie F, Garfinkel A, Weiss J N 2000 Annals of Biomedical Engineering 28 755

  • [1]

    Fenton F H, Cherry E M, Hasting H M 2002 Chaos 12 852

    [2]

    Cross M C, Hohenberg P C 1993 Rev. Mod. Phys. 65 851

    [3]

    Zaikin A N, Zhabotinsky A M 1970 Nature 225 535

    [4]

    Br M, Kevrekidis I G, Rotermund H H, Ertl G 1995 Phys. Rev. E 52 R5739

    [5]

    Lee K J, Cox E C, Goldstein R E 1996 Phys. Rev. Lett. 76 1174

    [6]

    Qian Y, Song X Y, Shi W 2006 Acta Phys. Sin. 55 4420 (in chinese) [钱 郁 、宋宣玉、时 伟 2006 物理学报 55 4420]

    [7]

    Liu Fu 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 物理学报 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 物理学报 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 物理学报 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]

    Br M, Eiswirth M 1993 Phys. Rev. E 48 1635

    [16]

    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]

    [17]

    Wang S H, Choe W G, Lee K J 2000 Phys. Rev. E 62 4799

    [18]

    Tang D N, Tang G N 2010 Acta Phys. Sin. 59 2319 (in Chinese) [唐冬妮、唐国宁 2010物理学报 59 2319]

    [19]

    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 物理学报 57 5400]

    [20]

    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]

    [21]

    Ma J, Wang C N, Jin W Y, Li Y L, Pu Z S 2008 Chin. Phys. B 17 2844

    [22]

    Yang J Z, Zhang M 2005 Chin. Phys. Lett. 22 3195

    [23]

    Gerhardt M, Schuster H, Tyson J J 1990 Physica D 46 392

    [24]

    Weimar J R, Tyson J J, Watson L T 1992 Physica D 55 309

    [25]

    Greenberg J M, Hastings S P 1978 SIAM Journal on Applied Mathematics 34 515

    [26]

    Qu Z, Xie F, Garfinkel A, Weiss J N 2000 Annals of Biomedical Engineering 28 755

  • Citation:
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Publishing process
  • Received Date:  17 May 2010
  • Accepted Date:  06 July 2010
  • Published Online:  15 March 2011

The numerical study on the effect of the earlyafterdepolarization on spiral wavesin discrete excitable media

  • 1. College of Physics and Technology,Guangxi Normal University,Guilin 541004,China

Abstract: The early afterdepolarization (EAP) behavior is introduced into the Greeberg-Hasting model of discrete excitable medium through considering that some of the refractory states can be excited. The effect of the EAP on spiral wave is studied. The numerical results show that the EAP has significant influences on spiral waves when the related parameters are suitably chosen. These influences include that the EAP causes spiral wave drifting and meandering,and spiral breakup. The pattern of spiral wave is distorted. The spiral wave varies alternately between those with thick and thin arms. The period of spiral wave alters alternately between two values. The EAP induces the transition from stable spiral wave to breathing spiral wave or antispiral wave. When the excitation threshold of refractory states is very high,the EAP has no affect on the spiral wave. The EAP induced phenomena are briefly discussed.

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