|
|
Size transition of spiral waves using the pulse array method |
Xie Ling-Ling(谢玲玲) and Gao Ji-Hua(高继华)† |
Shenzhen Key Laboratory of Special Functional Materials, College of Materials, Shenzhen University, Shenzhen 518060, China |
|
|
Abstract The domain size of spiral waves is an important issue in studies of two-dimensional (2D) spatiotemporal patterns. In this work, we use the 2D complex Ginzburg--Landau equation (CGLE) as our model and find that an initially big spiral can successfully transfer to several small spirals by applying a pulse array method. The impacts of several important factors, such as array density, controlling intensity and pulsing time, are investigated. This control approach may be useful for the control of 2D spatiotemporal patterns and has potential applications in the control of some realistic systems, such as meteorological and cardiac systems.
|
Received: 19 November 2009
Accepted manuscript online:
|
PACS:
|
05.45.-a
|
(Nonlinear dynamics and chaos)
|
|
02.30.Jr
|
(Partial differential equations)
|
|
87.19.Hh
|
(Cardiac dynamics)
|
|
Cite this article:
Xie Ling-Ling(谢玲玲) and Gao Ji-Hua(高继华) Size transition of spiral waves using the pulse array method 2010 Chin. Phys. B 19 060516
|
[1] |
Diercks J W and Anthes R A 1976 J. Atmos. Sci. 33 959
|
[2] |
Winfree A T 1987 When Time Breaks Down (Cambridge: Princeton University Press)
|
[3] |
Yu L C, Ma J, Zhang G Y and Chen Y 2008 Chin. Phys. Lett. 25 2706
|
[4] |
Jakubith S, Rotermund H H, Engel W, Oertzen A von and Ertl G 1990 Phys. Rev. Lett. 65 3013
|
[5] |
Ecke R E, Hu Y, Mainieri R and Ahlers G 1995 Science 269 1704
|
[6] |
Vanag V K and Epstein I R 2001 Science 294 835
|
[7] |
Gong Y and Christini D J 2003 Phys. Rev. Lett. 90 088302
|
[8] |
Zaritski R M and Pertsov A M 2002 Phys. Rev. E 66 066120
|
[9] |
Goryachev A, Chate H and Kapral R 1998 Phys. Rev. Lett . 80 873
|
[10] |
Yuan G Y, Zhang G C, Wang G R and Chen S G 2005 Commun. Theor Phys. 43 459
|
[11] |
Xiao J H, Hu G and Hu B 2004 Chin. Phys. Lett. 21 1224
|
[12] |
Alonso S, Sagues F and Mikhailov A S 2003 Science 299 1722
|
[13] |
Zhang H, Hu B and Hu G 2003 Phys. Rev. E 68 026134
|
[14] |
Gan Z N, Ma J, Zhang G Y and Chen Y 2008 Acta Phys. Sin. 57 5400 (in Chinese)
|
[15] |
Bar M and Eiswirth M 1993 Phys. Rev. E 48 R1635
|
[16] |
Brusch L, Torcini A and Bar M 2003 Phys. Rev. Lett. 91 108302
|
[17] |
Ouyang Q and Flesselles J M 1996 Nature 379 143
|
[18] |
Bar M and Or-Guil M 1999 Phys. Rev. Lett. 82 1160
|
[19] |
Liu F C, Wang X F, Li X C and Dong L F 2007 Chin. Phys. 16 2640
|
[20] |
Yuan G Y, Yang S P, Wang G R and Chen S G 2008 Chin. Phys. B 17 1925
|
[21] |
Steinbock O, Schutze J and Muller S C 1992 Phys. Rev. Lett . 68 248
|
[22] |
Bohr T, Huber G and Ott E 1997 Physica D 106 95
|
[23] |
Zhan M, Luo J M and Gao J H 2007 Phys. Rev. E 75 016214
|
[24] |
Luo J M, Zhang B S and Zhan M 2009 Chaos 19 033133
|
[25] |
Hu G, Xiao J H, Chua L O and Pivka L 1998 Phys. Rev. Lett. 80 1884
|
[26] |
Kuramoto Y 1984 Chemical Oscillations, Waves and Turbulence (New York: Springer)
|
[27] |
Cross M and Hohenberg P 1993 Rev. Mod. Phys. 65 851
|
[28] |
Aranson I and Kramer L 2002 Rev. Mod. Phys . 74 99
|
[29] |
Hagan P S 1982 SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 42 762
|
[30] |
Gao J H and Zhan M 2007 Phys. Lett. A 371 96
|
[31] |
Eguiluz V, Hernandez-Garcia E and Piro O 1999 Int. J. Bifur. Chaos 9 2209
|
[32] |
Lugovtsov B A 2002 J. Appl. Mech. Ech. Phys. 13 237
|
No Suggested Reading articles found! |
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
Altmetric
|
blogs
Facebook pages
Wikipedia page
Google+ users
|
Online attention
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
View more on Altmetrics
|
|
|