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In this paper, we study the influence of the rewiring probability p of the directed small-world network on dynamical behavior of spiral wave using the Greenberg-Hastings cellular automaton model. The computer simulation results show that when p is small enough, the stable spiral wave under the regular networks keeps its stability unchanged, and when p is increased, the phenomenon such as meandering, breakup and disappearance of the spiral waves appears. The relation between the excitability and p leads to the conclusion that the occurrence of the above phenomenon originates from the reducing of the excitability. On the other hand, the period of cell is also related to p.
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Keywords:
- cellular automaton /
- spiral wave /
- excitable media /
- directed small-world network
[1] Newman M E J 2001 Phys. Rev. E 64 016131
[2] [3] Newman M E J 2001 Phys. Rev. E 64 016132
[4] Huberman B A, Adamic L A 1999 Nature 401 131
[5] [6] [7] Amaral L A N, Scala A, Barthelemy M, Stanley H E 2000 Proc. Natl. Acad. Sci. USA 97 11149
[8] [9] Williams R J, Martinez N D 2000 Nature 404 180
[10] [11] Watts D J, Strogatz S H 1998 Nature 393 440
[12] [13] Barabsi A L, Albert R 1999 Science 286 509
[14] Parisi G J 1986 Physica A 19 L675
[15] [16] Crisanti A, Falcioni M, Vulpiani A 1993 Physica A 26 3441
[17] [18] Snchez A D, Lpez J M, Rodrguez M A 2002 Phys. Rev. Lett. 88 048701
[19] [20] He D H, Hu G, Zhan M, Ren W, Gao Z 2002 Phys. Rev. E 65 055204
[21] [22] [23] Qian Y, Liao X H, Huan X D, Mi Y Y, Zhang L S, Hu G 2010 Phys. Rev. E 82 026107
[24] Bai K Z, Tan H L, Kong L J, Liu M R 2010 Chin. Phys. B 19 040510
[25] [26] Li Q, Guo Q Y, Li R D 2006 Chin. Phys. B 15 778
[27] [28] Nishiyama A, Tanaka H, Tokihiro T 2008 Physica A 387 3129
[29] [30] Markus M, Hess B 1990 Nature 347 56
[31] [32] Bub G, Shrier A, Glass L 2005 Phys. Rev. Lett. 94 028105
[33] [34] [35] Zhang L S, Deng M Y, Kong L J, Liu M R, Tang G N 2009 Acta Phys. Sin. 58 4493 (in Chinese)[张立升、 邓敏艺、 孔令江、 刘慕仁、 唐国宁 2009 物理学报 58 4493]
[36] [37] 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]
[38] Greenberg J M, Hastings S P 1978 SIAM J. Appl. Math. 34 515
[39] -
[1] Newman M E J 2001 Phys. Rev. E 64 016131
[2] [3] Newman M E J 2001 Phys. Rev. E 64 016132
[4] Huberman B A, Adamic L A 1999 Nature 401 131
[5] [6] [7] Amaral L A N, Scala A, Barthelemy M, Stanley H E 2000 Proc. Natl. Acad. Sci. USA 97 11149
[8] [9] Williams R J, Martinez N D 2000 Nature 404 180
[10] [11] Watts D J, Strogatz S H 1998 Nature 393 440
[12] [13] Barabsi A L, Albert R 1999 Science 286 509
[14] Parisi G J 1986 Physica A 19 L675
[15] [16] Crisanti A, Falcioni M, Vulpiani A 1993 Physica A 26 3441
[17] [18] Snchez A D, Lpez J M, Rodrguez M A 2002 Phys. Rev. Lett. 88 048701
[19] [20] He D H, Hu G, Zhan M, Ren W, Gao Z 2002 Phys. Rev. E 65 055204
[21] [22] [23] Qian Y, Liao X H, Huan X D, Mi Y Y, Zhang L S, Hu G 2010 Phys. Rev. E 82 026107
[24] Bai K Z, Tan H L, Kong L J, Liu M R 2010 Chin. Phys. B 19 040510
[25] [26] Li Q, Guo Q Y, Li R D 2006 Chin. Phys. B 15 778
[27] [28] Nishiyama A, Tanaka H, Tokihiro T 2008 Physica A 387 3129
[29] [30] Markus M, Hess B 1990 Nature 347 56
[31] [32] Bub G, Shrier A, Glass L 2005 Phys. Rev. Lett. 94 028105
[33] [34] [35] Zhang L S, Deng M Y, Kong L J, Liu M R, Tang G N 2009 Acta Phys. Sin. 58 4493 (in Chinese)[张立升、 邓敏艺、 孔令江、 刘慕仁、 唐国宁 2009 物理学报 58 4493]
[36] [37] 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]
[38] Greenberg J M, Hastings S P 1978 SIAM J. Appl. Math. 34 515
[39]
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