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The experimental results confirmin that spiral wave can be observed in the cortex of brain and the electric signals in neurons can proprgate with spiral wave. The mechanism for the formation of spiral wave is investiaged in the regular network of Hodgkin-Huxley, which can measure the effect of ion channels, and the sprial waves with different periods are developed to occupy the network by blocking the travelling wave with defects. The basic condition for inducing spiral wave and the effect of the couling intensity are analyzed. The potential mechanism for developing spiral wave is discussed.
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Keywords:
- meuronal network /
- travelling wave /
- defects /
- spiral wave
[1] Biktashev V N, Holden A V 1998 Chaos 8 48
[2] Ouyang Q, Felesselles J M 1996 Nature 379 143
[3] Ouyang Q, Swinney H L, Li G 2000 Phys. Rev. Lett. 84 1047
[4] Zhou L Q, Ouyang Q 2000 Phys. Rev. Lett. 85 1650
[5] Fenton F H, Cherry E M, Hastings H M 2002 Chaos 12 852
[6] Stamp A T, Osipov G V, Collins J J 2002 Chaos 12 931.
[7] Bär M, Brusch L, Or-Guil M 2004 Phys. Rev. Lett. 92 119801
[8] Fu Y Q, Zhang H, Cao Z J 2005 Phys. Rev. E 72 046206.
[9] Zhang H, Chen J X, Li Y Q 2006 J. Chem. Phys. 125 204503
[10] Ma J, Ying H, Li Y L 2007 Chin. Phys. 16 955
[11] Chen J X, Hu BB 2008 Europhys Lett. 84 34002
[12] Chen J X, Xu J R, Yuan X P 2009 J. Phys. Chem. B 11 849
[13] Tang D N, Zhang X, Ren W 2010 Acta. Phys. Sin. 59 2319 (in Chinese) [唐冬妮, 张旭, 任卫等 2010 59 2319]
[14] Wei H M, Tang G N 2011 Acta. Phys. Sin. 60 030501 (in Chinese) [韦海明, 唐国宁 2011 60 030501]
[15] Wei H M, Tang G N 2011 Acta. Phys. Sin. 60 040504 (in Chinese) [韦海明, 唐国宁 2011 60 040504]
[16] Dong L F, Bai Z G, He Y F 2012 Acta. Phys. Sin. 61 120509 (in Chinese) [董丽芳, 白占国, 贺亚峰 2012 61 120509]
[17] Ma J, Jia Y, Wang C N 2008 J. Phys. A 41 385105
[18] Wang C N, Yang L J, Yuan L H 2010 Communications in Nonlinear Science and Numerical Simulation 15 3913
[19] Ma J, Tang J 2011 Optimal Control for Patterns in Space-time System (Wuhan: Huazhong University of Science and Technology Publishing House) p12 (in Chinese) [马军, 唐军, 时空系统斑图优化控制 (武汉: 华中科技大学出版社) 第12页]
[20] Huang X Y, Troy W C, Yang Q 2004 J. Neurosci 24 9897
[21] Schiff S J, Huang X Y, Wu J Y 2007 Phys. Rev. Lett. 98 178102
[22] He D H, Shi P L, Stone L W 2003 Phys. Rev. E 67 27201
[23] Ma J, Ying H P, Liu Y 2009 Chin. Phys. B 18 98
[24] Perc M 2007 Chaos, Solitons & Fractals 31 280
[25] Wang Q Y, Perc M, Duan Z S 2008 Phys. Lett. A 372 5681
[26] Gonze D, Bernard S, Waltermann C 2005 Bio. Phys. J. 89 120
[27] Wang C N, Ma J, Tang J 2010 Commun. Theor. Phys. 53 382
[28] Ma J, Wang C N, Jin W Y 2010 Appl. Math. Comput. 217 3844
[29] Ma J, Tang J, Zhang A H 2010 Sci. China Phys. Mech. Astro. 53 672
[30] Ma J, Wu Y, Ying H P 2011 Chin. Sci. Bull. 56 151
[31] Ma J, Huang L, Ying H P 2012 Chin. Sci. Bull. 57 2094
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[1] Biktashev V N, Holden A V 1998 Chaos 8 48
[2] Ouyang Q, Felesselles J M 1996 Nature 379 143
[3] Ouyang Q, Swinney H L, Li G 2000 Phys. Rev. Lett. 84 1047
[4] Zhou L Q, Ouyang Q 2000 Phys. Rev. Lett. 85 1650
[5] Fenton F H, Cherry E M, Hastings H M 2002 Chaos 12 852
[6] Stamp A T, Osipov G V, Collins J J 2002 Chaos 12 931.
[7] Bär M, Brusch L, Or-Guil M 2004 Phys. Rev. Lett. 92 119801
[8] Fu Y Q, Zhang H, Cao Z J 2005 Phys. Rev. E 72 046206.
[9] Zhang H, Chen J X, Li Y Q 2006 J. Chem. Phys. 125 204503
[10] Ma J, Ying H, Li Y L 2007 Chin. Phys. 16 955
[11] Chen J X, Hu BB 2008 Europhys Lett. 84 34002
[12] Chen J X, Xu J R, Yuan X P 2009 J. Phys. Chem. B 11 849
[13] Tang D N, Zhang X, Ren W 2010 Acta. Phys. Sin. 59 2319 (in Chinese) [唐冬妮, 张旭, 任卫等 2010 59 2319]
[14] Wei H M, Tang G N 2011 Acta. Phys. Sin. 60 030501 (in Chinese) [韦海明, 唐国宁 2011 60 030501]
[15] Wei H M, Tang G N 2011 Acta. Phys. Sin. 60 040504 (in Chinese) [韦海明, 唐国宁 2011 60 040504]
[16] Dong L F, Bai Z G, He Y F 2012 Acta. Phys. Sin. 61 120509 (in Chinese) [董丽芳, 白占国, 贺亚峰 2012 61 120509]
[17] Ma J, Jia Y, Wang C N 2008 J. Phys. A 41 385105
[18] Wang C N, Yang L J, Yuan L H 2010 Communications in Nonlinear Science and Numerical Simulation 15 3913
[19] Ma J, Tang J 2011 Optimal Control for Patterns in Space-time System (Wuhan: Huazhong University of Science and Technology Publishing House) p12 (in Chinese) [马军, 唐军, 时空系统斑图优化控制 (武汉: 华中科技大学出版社) 第12页]
[20] Huang X Y, Troy W C, Yang Q 2004 J. Neurosci 24 9897
[21] Schiff S J, Huang X Y, Wu J Y 2007 Phys. Rev. Lett. 98 178102
[22] He D H, Shi P L, Stone L W 2003 Phys. Rev. E 67 27201
[23] Ma J, Ying H P, Liu Y 2009 Chin. Phys. B 18 98
[24] Perc M 2007 Chaos, Solitons & Fractals 31 280
[25] Wang Q Y, Perc M, Duan Z S 2008 Phys. Lett. A 372 5681
[26] Gonze D, Bernard S, Waltermann C 2005 Bio. Phys. J. 89 120
[27] Wang C N, Ma J, Tang J 2010 Commun. Theor. Phys. 53 382
[28] Ma J, Wang C N, Jin W Y 2010 Appl. Math. Comput. 217 3844
[29] Ma J, Tang J, Zhang A H 2010 Sci. China Phys. Mech. Astro. 53 672
[30] Ma J, Wu Y, Ying H P 2011 Chin. Sci. Bull. 56 151
[31] Ma J, Huang L, Ying H P 2012 Chin. Sci. Bull. 57 2094
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