螺旋波动力学性质的元胞自动机有向小世界网络研究

田昌海; 邓敏艺; 孔令江; 刘慕仁

doi:10.7498/aps.60.080505

摘要

以Greenberg-Hastings激发介质元胞自动机模型为基础,研究了有向小世界网络中重新连接概率p对螺旋波动力学行为的影响.对于在规则网络下的稳定螺旋波,施加有向小世界网络后发现:当p值较小时,原本稳定的螺旋波仍保持其稳定性.随着p的增大,先后观察到螺旋波持续漫游、螺旋波断裂以及螺旋波消失等现象.通过监测系统的激发比率,发现以上现象的产生源于介质激发性随p的增大而降低.同时还发现元胞周期的变化也与p有关.

关键词:

Abstract

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.

Keywords:

作者及机构信息

1.
广西师范大学物理科学与技术学院,桂林 541004;

2.
广西师范学院物理与电子工程学院,南宁 530000

基金项目: 国家自然科学基金(批准号: 10765002,10962002,81060307)资助的课题.

Authors and contacts

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

2.
College of Physics and Electronic Engineering, Guangxi Teachers Education University, Nanning 530000, China

参考文献

[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]

施引文献

[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]

计量

文章访问数: 6499
PDF下载量: 1009
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板