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The influence of the defects without diffusion function on dynamics of spiral wave

Tang Dong-Ni Tang Guo-Ning

The influence of the defects without diffusion function on dynamics of spiral wave

Tang Dong-Ni, Tang Guo-Ning
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  • The Br model is considered. The influence of the defect, defined by failure of the diffusion effect, on dynamics of spiral wave is investigated by introducing in to the system some defects. These defects are uniformly distributed. It was found numerically that these defects can lead to the reduction of the excitability of medium and the wave speed. When the number of defects is large enough, these defects can induce the meandering or the breakage of an originally stable spiral wave. On the other hands, the defects can yet cause an unstable spiral wave to become a rigidly rotating or meandering spiral wave. The phenomenon that Doppler effect causes unstable spiral wave to break up into co-existing states of spatiotemporal chaos and small spiral waves is observed for the first time. The physical mechanism of these phenomena are briefly discussed.
    • Funds:
    [1]

    [1]Ouyang Q 2000 Pattern Formation in Reaction-Diffusion Systems (Shanghai: Shang Scientific and Technological Education Publishing House) p73—78 (in Chinese)[欧阳颀 2000 反应扩散系统中螺旋波的失稳 (上海:上海科技教育出版社) 第73—78页]

    [2]

    [2]Jakubith S, Rotermund H H, Engel W, Oertzen A V, Erth G 1990 Phys. Rev. Lett. 65 859

    [3]

    [3]Henry H 2004 Phys. Rev. E 70 026204

    [4]

    [4]Nash M P, Panfilov A V 2004 Prog. Biophys. Molec. Biol. 85 501

    [5]

    [5]Zhang H, Hu B, Hu G 2003 Phys. Rev. E 68 026134

    [6]

    [6]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、李廷龙 2008 物理学报 57 2832]

    [7]

    [7]Ma J, Jin W Y, Li Y L, Chen Y 2007 Acta Phys. Sin. 56 2456 (in Chinese)[马军、靳伍银、李廷龙、陈勇 2007 物理学报 56 2456]

    [8]

    [8]Yin X Z, Liu Y 2008 Acta Phys. Sin. 57 6844 (in Chinese)[尹小舟、刘勇 2008 物理学报 57 6844]

    [9]

    [9]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]

    [10]

    ]Steinbock O, Muller S C 1993 Phys. Rev. E 47 1506

    [11]

    ]Munuzuri A P, Perez-Munuzuri V, Perez-Villar V 1998 Phys. Rev. E 58 R2689

    [12]

    ]Li B W, Zhang H, Ying H P, Hu G 2009 Phys. Rev. E 79 026220

    [13]

    ]Ten Tusscher K H W J, Panfilov A V 2003 Phys. Rev. E 68 062902

    [14]

    ]Shajahan T K, Sinha S, Pandit R 2007 Phys. Rev. E 75 011929

    [15]

    ]Dai Y, Tang G N 2009 Acta Phys. Sin. 58 1491 (in Chinese)[戴瑜、唐国宁 2009 物理学报 58 1491]

    [16]

    ]Br M and Eiswirth M 1993 Phys. Rev. E 48 R1635

  • [1]

    [1]Ouyang Q 2000 Pattern Formation in Reaction-Diffusion Systems (Shanghai: Shang Scientific and Technological Education Publishing House) p73—78 (in Chinese)[欧阳颀 2000 反应扩散系统中螺旋波的失稳 (上海:上海科技教育出版社) 第73—78页]

    [2]

    [2]Jakubith S, Rotermund H H, Engel W, Oertzen A V, Erth G 1990 Phys. Rev. Lett. 65 859

    [3]

    [3]Henry H 2004 Phys. Rev. E 70 026204

    [4]

    [4]Nash M P, Panfilov A V 2004 Prog. Biophys. Molec. Biol. 85 501

    [5]

    [5]Zhang H, Hu B, Hu G 2003 Phys. Rev. E 68 026134

    [6]

    [6]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、李廷龙 2008 物理学报 57 2832]

    [7]

    [7]Ma J, Jin W Y, Li Y L, Chen Y 2007 Acta Phys. Sin. 56 2456 (in Chinese)[马军、靳伍银、李廷龙、陈勇 2007 物理学报 56 2456]

    [8]

    [8]Yin X Z, Liu Y 2008 Acta Phys. Sin. 57 6844 (in Chinese)[尹小舟、刘勇 2008 物理学报 57 6844]

    [9]

    [9]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]

    [10]

    ]Steinbock O, Muller S C 1993 Phys. Rev. E 47 1506

    [11]

    ]Munuzuri A P, Perez-Munuzuri V, Perez-Villar V 1998 Phys. Rev. E 58 R2689

    [12]

    ]Li B W, Zhang H, Ying H P, Hu G 2009 Phys. Rev. E 79 026220

    [13]

    ]Ten Tusscher K H W J, Panfilov A V 2003 Phys. Rev. E 68 062902

    [14]

    ]Shajahan T K, Sinha S, Pandit R 2007 Phys. Rev. E 75 011929

    [15]

    ]Dai Y, Tang G N 2009 Acta Phys. Sin. 58 1491 (in Chinese)[戴瑜、唐国宁 2009 物理学报 58 1491]

    [16]

    ]Br M and Eiswirth M 1993 Phys. Rev. E 48 R1635

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    [9] Chen Yong, Jin Wu-Yin, Ma Jun, Li Yan-Long. Suppression of meandering spiral waves in the excitable media due to a perturbation with stochastic phase. Acta Physica Sinica, 2007, 56(4): 2456-2465. doi: 10.7498/aps.56.2456
    [10] Dong Li-Fang, Bai Zhan-Guo, He Ya-Feng. Sparse and dense spiral waves in heterogeneous excitable media. Acta Physica Sinica, 2012, 61(12): 120509. doi: 10.7498/aps.61.120509
    [11] Zhou Zhen-Wei, Chen Xing-Ji, Tian Tao-Tao, Tang Guo-Ning. Study on the control of spiral waves in coupled excitable media. Acta Physica Sinica, 2012, 61(21): 210506. doi: 10.7498/aps.61.210506
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  • Received Date:  23 June 2009
  • Accepted Date:  20 July 2009
  • Published Online:  15 April 2010

The influence of the defects without diffusion function on dynamics of spiral wave

  • 1. 广西师范大学物理科学与技术学院,桂林 541004

Abstract: The Br model is considered. The influence of the defect, defined by failure of the diffusion effect, on dynamics of spiral wave is investigated by introducing in to the system some defects. These defects are uniformly distributed. It was found numerically that these defects can lead to the reduction of the excitability of medium and the wave speed. When the number of defects is large enough, these defects can induce the meandering or the breakage of an originally stable spiral wave. On the other hands, the defects can yet cause an unstable spiral wave to become a rigidly rotating or meandering spiral wave. The phenomenon that Doppler effect causes unstable spiral wave to break up into co-existing states of spatiotemporal chaos and small spiral waves is observed for the first time. The physical mechanism of these phenomena are briefly discussed.

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