Please wait a minute...
Chin. Phys. B, 2014, Vol. 23(5): 050502    DOI: 10.1088/1674-1056/23/5/050502
GENERAL Prev   Next  

Motion of spiral tip driven by local forcing in excitable media

Liu Gui-Quan (刘贵泉)a b, Ying He-Ping (应和平)a
a Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 310027, China;
b College of Science, China Jiliang University, Hangzhou 310018, China
Abstract  We study the motion of a spiral wave controlled by a local periodic forcing imposed on a region around the spiral tip in an excitable medium. Three types of trajectories of spiral tip are observed: the epicycloid-like meandering, the resonant drift, and the hypocycloid-like meandering. The frequency of the spiral is sensitive to the local periodic forcing. The dependency of spiral frequency on the amplitude and size of local periodic forcing are presented. In addition, we show how the drift speed and direction are adjusted by the amplitude and phase of local periodic forcing, which is consistent with a theoretical analysis based on the weak deformation approximation.
Keywords:  spiral wave      local forcing      resonant drift      weak deformation approximation  
Received:  10 October 2013      Revised:  25 November 2013      Accepted manuscript online: 
PACS:  05.45.-a (Nonlinear dynamics and chaos)  
  05.45.Xt (Synchronization; coupled oscillators)  
  82.40.Ck (Pattern formation in reactions with diffusion, flow and heat transfer)  
  82.20.-w (Chemical kinetics and dynamics)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11274271) and the Scientific Research Foundation of Education Bureau of Zhejiang Province, China (Grant No. Y201224250).
Corresponding Authors:  Liu Gui-Quan, Ying He-Ping     E-mail:  gqliu@zju.edu.cn;hpying@zju.edu.cn
About author:  05.45.-a; 05.45.Xt; 82.40.Ck; 82.20.-w

Cite this article: 

Liu Gui-Quan (刘贵泉), Ying He-Ping (应和平) Motion of spiral tip driven by local forcing in excitable media 2014 Chin. Phys. B 23 050502

[1] Meron E 1992 Phys. Rep. 218 1
[2] Lechleiter J, Girard S, Peralta E and Clapham D 1991 Science 252 123
[3] Davidenko J, Pertsov A, Salomonsz R, Baxter W and Jalife J 1992 Nature 355 349
[4] Plapp B B, Egolf D A, Bodenschatz E and Pesch W 1998 Phys. Rev. Lett. 81 5334
[5] Winfree T 1991 Chaos 1 303
[6] Steinbock O, Zykov V and Müller S C 1993 Nature 366 322
[7] Ouyang Q and Flesselles J M 1996 Nature 379 143
[8] Jahuke W and Winfree A T 1991 Int. J. Bifurc. Chaos 1 445
[9] Zykov V S, Steinbock O and Müller S C 1994 Chaos 4 509
[10] Guo H, Liao H M and Ouyang Q 2002 Phys. Rev. E 66 026104
[11] Zhan M, Wang X G, Gong X F and Lai C H 2005 Phys. Rev. E 71 036212
[12] Mantel R M and Barkley D 1996 Phys. Rev. E 54 4791
[13] Zhang H, Cao Z J, Wu N J, Ying H P and Hu G 2005 Phys. Rev. Lett. 94 188301
[14] Yuan G Y, Wang G R and Chen S G 2005 Europhys. Lett. 72 908
[15] Wu N J, Zhang H, Ying H P, Cao Z J and Hu G 2006 Phys. Rev. E 73 060901
[16] Zykov S, Zykov V and Davydov V 2006 Europhys. Lett. 73 335
[17] Yu L C, Ma J, Zhang G Y and Chen Y 2008 Chin. Phys. Lett. 25 2706
[18] Zykov V S, Bordiougov G, Brandtstädter H, Gerdes I and Engel H 2004 Phys. Rev. Lett. 92 018304
[19] Zhang H, Wu N J, Ying H P, Hu G and Hu B B 2004 J. Chem. Phys. 121 7276
[20] Liu G Q, Wu N J and Ying H P 2013 Commun. Nonlinear Sci. Numer. Simulat. 18 2398
[21] Steinbock O, Schütze J and Müller S C 1992 Phys. Rev. Lett. 68 248
[22] Munuzuri A P, Gesteira M G and Munuzuri V P 1994 Phys. Rev. E 50 4258
[23] Chen J X and Hu B B 2008 Europhysics. Lett. 84 34002
[24] Lou Q, Chen J X, Zhao Y H, Shen F R, Fu Y, Wang L L and Liu Y 2012 Phys. Rev. E 85 026213
[25] Grill S, Zykov V S and Müller S C 1995 Phys. Rev. Lett. 75 3368
[26] Zykov V S, Mikhailov A S and Müller S C 1990 Phys. Rev. Lett. 78 3398
[27] Ott E, Grebogi C and Yorke J A 1990 Phys. Rev. Lett. 64 1196
[28] Yuan G Y, Xu A G, Wang G R and Chen S G 2010 Europhys. Lett. 90 10013
[29] Zhang G Y, Ma J, Yu L C and Chen Y 2008 Chin. Phys. B 17 4107
[30] Yuan G Y, Yang S P, Wang G R and Chen S G 2005 Acta Phys. Sin. 54 1510 (in Chinese)
[31] Zhang H J, Wang P Y and Zhao Y Y 2005 Chin. Phys. Lett. 22 287
[32] Deng B W, Zhang G Y and Chen Y 2008 Commun. Theor. Phys. 52 173
[33] Ma J, Wang C N, Jin W Y, Li Y L and Pu Z S 2008 Chin. Phys. B 17 2844
[34] Wu N J, Gao H J and Ying H P 2010 Phys. Rev. E 82 066206
[35] Markus M, Magy-Ungvaray Z and Hess B 1992 Science 257 225
[36] Xu L D, Qu Z L and Di Z R 2009 Phys. Rev. E 79 036212
[37] Xu L D, Li Z, Qu Z L and Di Z R 2012 Phys. Rev. E 85 046216
[38] Chen J X, Xu J R, Zhang X P, Zhang J W and Zhang X W 2009 Cent. Eur. J. Phys. 7 108
[39] Cao Z J, Li P F, Zhang H and Hu G 2007 Chaos 17 0151071
[40] Chen J X, Mao J W, He Y F, Hu B B, Xu J R and Yuan X P 2009 Phys. Rev. E 79 066209
[41] Zykov S, Zykov V S and Davydov V 2006 Europhys. Lett. 73 335
[42] Wu N J, Li B W and Ying H P 2006 Chin. Phys. Lett. 23 2030
[1] Applying a global pulse disturbance to eliminate spiral waves in models of cardiac muscle
Jian Gao(高见), Changgui Gu(顾长贵), and Huijie Yang(杨会杰). Chin. Phys. B, 2021, 30(7): 070501.
[2] Unpinning the spiral waves by using parameter waves
Lu Peng(彭璐) and Jun Tang(唐军). Chin. Phys. B, 2021, 30(5): 058202.
[3] Exploring the role of inhibitory coupling in duplex networks
Cui-Yun Yang(杨翠云), Guo-Ning Tang(唐国宁), Hai-Ying Liu(刘海英). Chin. Phys. B, 2017, 26(8): 088201.
[4] Effects of abnormal excitation on the dynamics of spiral waves
Min-Yi Deng(邓敏艺), Xue-Liang Zhang(张学良), Jing-Yu Dai(戴静娱). Chin. Phys. B, 2016, 25(1): 010504.
[5] A cellular automaton model for the ventricular myocardium considering the layer structure
Deng Min-Yi (邓敏艺), Dai Jing-Yu (戴静娱), Zhang Xue-Liang (张学良). Chin. Phys. B, 2015, 24(9): 090503.
[6] The effect of cellular aging on the dynamics of spiral waves
Deng Min-Yi (邓敏艺), Chen Xi-Qiong (陈茜琼), Tang Guo-Ning (唐国宁). Chin. Phys. B, 2014, 23(12): 120503.
[7] The influence of long-range links on spiral waves and its application for control
Qian Yu (钱郁). Chin. Phys. B, 2012, 21(8): 088201.
[8] Elimination of spiral waves and spatiotemporal chaos by the synchronization transmission technology of network signals
Zhang Qing-Ling(张庆灵), Lü Ling(吕翎), and Zhang Yi(张翼) . Chin. Phys. B, 2011, 20(9): 090514.
[9] Spiral-wave dynamics in excitable medium with excitability modulated by rectangle wave
Yuan Guo-Yong(袁国勇) . Chin. Phys. B, 2011, 20(4): 040503.
[10] Synchronizing spiral waves in a coupled Rössler system
Gao Jia-Zhen(高加振), Yang Shu-Xin(杨舒心), Xie Ling-Ling(谢玲玲), and Gao Ji-Hua(高继华) . Chin. Phys. B, 2011, 20(3): 030505.
[11] Lattice Boltzmann simulation for the energy and entropy of excitable systems
Deng Min-Yi(邓敏艺), Tang Guo-Ning(唐国宁), Kong Ling-Jiang(孔令江), and Liu Mu-Ren(刘慕仁) . Chin. Phys. B, 2011, 20(2): 020510.
[12] Size transition of spiral waves using the pulse array method
Xie Ling-Ling(谢玲玲) and Gao Ji-Hua(高继华). Chin. Phys. B, 2010, 19(6): 060516.
[13] 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). Chin. Phys. B, 2010, 19(5): 050513.
[14] Distributed predictive control of spiral wave in cardiac excitable media
Gan Zheng-Ning(甘正宁) and Cheng Xin-Ming(成新明). Chin. Phys. B, 2010, 19(5): 050514.
[15] Controlling intracellular Ca2+ spiral waves by the local agonist in the cell membrane
Qiu Kang(仇康), Tang Jun(唐军), Ma Jun(马军), and Luo Ji-Ming(罗继明). Chin. Phys. B, 2010, 19(3): 030508.
No Suggested Reading articles found!