Please wait a minute...
Chin. Phys. B, 2010, Vol. 19(5): 050513    DOI: 10.1088/1674-1056/19/5/050513
GENERAL Prev   Next  

Doppler instability of antispiral waves in discrete oscillatory reaction-diffusion media

Qian Yu(钱郁), Huang Xiao-Dong(黄晓东), Liao Xu-Hong(廖旭红), and Hu Gang(胡岗)
Department of Physics, Beijing Normal University, Beijing 100875, China
Abstract  This paper investigates antispiral wave breakup phenomena in coupled two-dimensional FitzHugh--Nagumo cells with self-sustained oscillation via Hopf bifurcation. When the coupling strength of the active variable decreases to a critical value, wave breakup phenomenon first occurs in the antispiral core region where waves collide with each other and spontaneously break into spatiotemporal turbulence. Measurements reveal for the first time that this breakup phenomenon is due to the mechanism of antispiral Doppler instability.
Keywords:  antispiral waves      break up      Doppler instability  
Received:  22 September 2009      Revised:  20 October 2009      Accepted manuscript online: 
PACS:  87.17.Jj (Cell locomotion, chemotaxis)  
  87.15.R- (Reactions and kinetics)  
  87.18.Hf (Spatiotemporal pattern formation in cellular populations)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No.~10675020) and by the National Basic Research Program of China (973 Program) (Grant No.~2007CB814800).

Cite this article: 

Qian Yu(钱郁), Huang Xiao-Dong(黄晓东), Liao Xu-Hong(廖旭红), and Hu Gang(胡岗) Doppler instability of antispiral waves in discrete oscillatory reaction-diffusion media 2010 Chin. Phys. B 19 050513

[1] Winfree A T 1987 When Time Breaks Down (Princeton:Princeton University Press)
[2] Kapral R and Showalter K 1995 Chemical Waves and Pat-tern (Dordrecht: Kluwer)
[3] Murray J 1989 Mathematical Biology (Berlin: Springer)
[4] Yamada T and Kuramoto Y 1976 Prog. Theor. Phys. 55 2035
[5] Selpuchre J A, Dewel G and Babloyantz A 1990 Phys.Lett. A 147 380
[6] Vanag V K and Epstein I R 2001 Science 294 835
[7] Vanag V K and Epstein I R 2001 Phys. Rev. Lett. 87 228301
[8] Vanag V K and Epstein I R 2002 Phys. Rev. Lett. 88 088303
[9] Gong Y F and Christini D J 2003 Phys. Rev. Lett. 90 088302
[10] Brush L, Nicola E M and B¨ar M 2004 Phys. Rev. Lett. 92 089901
[11] Nicola E M, Brush L and B¨ar M 2004 J. Phys. Chem. B 108 14733
[12] Cao Z J, Zhang H and Hu G 2007 Europhys. Lett. 79 34002
[13] Cui X H, Huang X Q, Cao Z J, Zhang H and Hu G 2008 Phys. Rev. E 78 026202
[14] Shao X, Wu Y B, Zhang J Z, Wang H L and Ouyang Q 2008 Phys. Rev. Lett. 100 198304
[15] Cross M C and Hohenberg P C 1993 Rev. Mod. Phys. 65 851
[16] Barkley D, Kness M and Tuckerman L 1990 Phys. Rev. A 44 2489
[17] B¨ar M and Eiswirth M 1993 Phys. Rev. E 48 1635
[18] Li G, Ouyang Q, Petrov V and Swinney H L 1996 Phys. Rev. Lett. 77 2105
[19] Ouyang Q, Swinney H L and Li G 2000 Phys. Rev. Lett. 84 1047
[20] Tobia S M and Knobloch E 1998 Phys. Rev. Lett. 80 4811
[21] Zhou L Q and Ouyang Q 2000 Phys. Rev. Lett. 85 1650
[22] Sandstede B and Scheel A 2000 Phys. Rev. E 62 7708
[23] Aranson I S and Kramer K 2002 Rev. Mod. Phys 74 99
[24] Weiss J N, Karagueuzian H S, Qu Z L and Chen P S 1999 Circulation 99 2819
[25] B¨ar M and Guil M O 1999 Phys. Rev. Lett. 82 1160
[26] Yang J Z, Xie F G, Qu Z L and Garlinkel A 2003 Phys.Rev. Lett. 91 148302
[27] Xie F G, Xie D Z and Weiss J N 2006 Phys. Rev. E 74 026107
[28] FitzHugh R A 1961 Biophys. J. 1 445
[1] Speedup of self-propelled helical swimmers in a long cylindrical pipe
Ji Zhang(张骥), Kai Liu(刘凯), and Yang Ding(丁阳). Chin. Phys. B, 2022, 31(1): 014702.
[2] Simulation of microswimmer hydrodynamics with multiparticle collision dynamics
Andreas Z?ttl. Chin. Phys. B, 2020, 29(7): 074701.
[3] Influence of matrix-metalloproteinase inhibitor on the interaction between cancer cells and matrigel
Teng Ye(叶腾), Fangfu Ye(叶方富), Feng Qiu(邱峰). Chin. Phys. B, 2020, 29(6): 068701.
[4] Influence of matrigel on the shape and dynamics of cancer cells
Teng Ye(叶腾), Feng Qiu(邱峰). Chin. Phys. B, 2019, 28(10): 108704.
[5] Diffusional inhomogeneity in cell cultures
Jia-Zheng Zhang(张佳政), Na Li(李娜), Wei Chen(陈唯). Chin. Phys. B, 2018, 27(2): 028705.
[6] In vitro three-dimensional cancer metastasis modeling: Past, present, and future
Wei-jing Han(韩伟静), Wei Yuan(袁伟), Jiang-rui Zhu(朱江瑞), Qihui Fan(樊琪慧), Junle Qu(屈军乐), Li-yu Liu(刘雳宇), on behalf of the U.S.--China Physical Sciences-Oncology Alliance. Chin. Phys. B, 2016, 25(1): 018709.
[7] Propulsive matrix of a helical flagellum
Zhang He-Peng (张何朋), Liu Bin (刘斌), Bruce Rodenborn, Harry L. Swinney. Chin. Phys. B, 2014, 23(11): 114703.
[8] A population-level model from the microscopic dynamics in Escherichia coli chemotaxis via Langevin approximation
He Zhuo-Ran (贺卓然), Wu Tai-Lin (吴泰霖), Ouyang Qi (欧阳颀), Tu Yu-Hai (涂豫海). Chin. Phys. B, 2012, 21(9): 098701.
No Suggested Reading articles found!