The influence of long-range links on spiral waves and its application for control

doi:10.1088/1674-1056/21/8/088201

中国物理B ›› 2012, Vol. 21 ›› Issue (8): 88201-088201.doi: 10.1088/1674-1056/21/8/088201

• INTERDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY • 上一篇下一篇

The influence of long-range links on spiral waves and its application for control

钱郁

Nonlinear Research Institute, Baoji University of Arts and Sciences, Baoji 721007, China

收稿日期:2012-02-02 修回日期:2012-02-29 出版日期:2012-07-01 发布日期:2012-07-01
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 11105003) and the Science Foundation of the Education Bureau of Shaanxi Province of China (Grant No. 11JK0544).

The influence of long-range links on spiral waves and its application for control

Qian Yu (钱郁)

Nonlinear Research Institute, Baoji University of Arts and Sciences, Baoji 721007, China

Received:2012-02-02 Revised:2012-02-29 Online:2012-07-01 Published:2012-07-01
Contact: Qian Yu E-mail:qianyu0272@163.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 11105003) and the Science Foundation of the Education Bureau of Shaanxi Province of China (Grant No. 11JK0544).

摘要/Abstract

摘要： The influence of long-range links on spiral waves in excitable medium has been investigated. Spatiotemporal dynamics in excitable small-world network transforms remarkably when we increase the long-range connection probability P. Spiral waves with few perturbations, broken spiral waves, pseudo spiral turbulence, synchronous oscillations, and homogeneous rest state are discovered under different network structures. Tip number is selected to detect non-equilibrium phase transition between different spatiotemporal patterns. The Kuramoto order parameter is used to identify these patterns and explain the emergence of the rest state. Finally, we use long-range links to control spiral wave and spiral turbulence successfully.

关键词: spiral waves, long-range link, spiral and turbulence control

Abstract: The influence of long-range links on spiral waves in excitable medium has been investigated. Spatiotemporal dynamics in excitable small-world network transforms remarkably when we increase the long-range connection probability P. Spiral waves with few perturbations, broken spiral waves, pseudo spiral turbulence, synchronous oscillations, and homogeneous rest state are discovered under different network structures. Tip number is selected to detect non-equilibrium phase transition between different spatiotemporal patterns. The Kuramoto order parameter is used to identify these patterns and explain the emergence of the rest state. Finally, we use long-range links to control spiral wave and spiral turbulence successfully.

Key words: spiral waves, long-range link, spiral and turbulence control

中图分类号: (Pattern formation in reactions with diffusion, flow and heat transfer)

82.40.Ck

05.65.+b (Self-organized systems) 89.75.Hc (Networks and genealogical trees)

钱郁. The influence of long-range links on spiral waves and its application for control[J]. 中国物理B, 2012, 21(8): 88201-088201.

Qian Yu (钱郁). The influence of long-range links on spiral waves and its application for control[J]. Chin. Phys. B, 2012, 21(8): 88201-088201.

参考文献 41

[1]	Lechleiter J, Girard S, Clapham D and Peralta E 1991 Nature 350 505
[2]	Glass L 1996 Phys. Today 45 40
[3]	Zaikin A N and Zhabotinsky A M 1970 Nature 225 535
[4]	Winfree A T 1972 Science 175 634
[5]	Ouyang Q and Flesselles J M 1996 Nature 379 143
[6]	Davidenko J M, Pertsov A V, Salomonsz R, Baxter W and Jalife J 1992 Nature 355 349
[7]	Kanakov O I, Osipov G V, Chan C K and Kurths J 2007 Chaos 17 015111
[8]	Huang X D, Qian Y, Zhang X M and Hu G 2010 Phys. Rev. E 81 051903
[9]	Grayalife R A, Pertsov A M and Jalife J 1998 Nature 392 75
[10]	Weiss J N, Garfinkel A, Karagueuzian H S, Qu Z L and Chen P S 1999 Circulation 99 2819
[11]	Gray R A 2002 Chaos 12 941
[12]	Aliev R R and Panfilov A V 1996 Chaos, Solitons and Fractals 7 293
[13]	Alonso S, Sagues F and Mikhailov A S 2003 Science 299 1772
[14]	Zhang H, Hu B and Hu G 2003 Phys. Rev. E 68 026134
[15]	Zhang H, Cao Z J, Wu N J, Ying H P and Hu G 2005 Phys. Rev. Lett. 94 188301
[16]	Xiao J H, Hu G, Zhang H and Hu B 2005 Europhys. Lett. 69 29
[17]	Qian Y, Song X Y, Shi W, Chen G Z and Xue Y 2006 Acta Phys. Sin. 55 4420 (in Chinese)
[18]	Ma J, Ying H P and Li Y L 2007 Chin. Phys. 16 955
[19]	Qiu K, Tang J, Ma J and Luo J M 2010 Chin. Phys. B 19 030508
[20]	Zhong M and Tang G N 2010 Acta Phys. Sin. 59 1593 (in Chinese)
[21]	Gao J Z, Xie L L, Xie W M and Gao J H 2011 Acta Phys. Sin. 60 080503 (in Chinese)
[22]	Jeong H, Mason S P, Barabasi A L and Oltvai Z N 2001 Nature 441 41
[23]	Camacho J, Guimera R and Amaral L N 2002 Phys. Rev. Lett. 88 228102
[24]	Bazhenov M, Timofeev I, Steriade M and Sejnowski T J 1999 Nature Neuroscience 2 168
[25]	Steriade M and Timofeev I 2003 Neuron 37 563
[26]	Buzsaki G and Draguhn A 2004 Science 304 1926
[27]	Mi Y Y, Zhang L S, Huang X D, Qian Y, Hu G and Liao X H 2011 Europhys. Lett. 95 58001
[28]	Hemmen J L 2004 Biol. Cybern. 91 347
[29]	Huang X Y, Troy W C, Yang Q, Ma H T, Laing C R, Schiff S J and Wu J X 2004 The Journal of Neuroscience 24 9897
[30]	Dahlem M A, Schneider F M and Schöll E 2008 Chaos 18 026110
[31]	Watts D J and Strogatz S H 1998 Nature 393 440
[32]	He D H, Hu G, Zhan M, Ren W and Gao Z 2002 Phys. Rev. E 65 055204R
[33]	Qi F, Hou Z H and Xin H W 2003 Phys. Rev. Lett. 91 064102
[34]	Roxin A, Riecke H and Solla S A 2004 Phys. Rev. Lett. 92 198101
[35]	Yonker S and Wackerbauer R 2006 Phys. Rev. E 73 055206
[36]	Sinha S, Saramäki J and Kaski K 2007 Phys. Rev. E 76 015101R
[37]	Qian Y, Huang X D, Hu G and Liao X H 2010 Phys. Rev. E 81 036101
[38]	Wang C N, Ma J, Tang J and Li Y L 2010 Commun. Theor. Phys. 53 382
[39]	Bär M and Eiswirth M 1993 Phys. Rev. E 48 1635R
[40]	Steele A J, Tinsley M and Showalter K 2006 Chaos 16 015110
[41]	Gray R A and Jalife J 1998 Chaos 8 65

The influence of long-range links on spiral waves and its application for control

The influence of long-range links on spiral waves and its application for control

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