Controlling the transition between Turing and antispiral patterns by using time-delayed-feedback

doi:10.1088/1674-1056/21/3/034701

中国物理B ›› 2012, Vol. 21 ›› Issue (3): 34701-034701.doi: 10.1088/1674-1056/21/3/034701

• ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS • 上一篇下一篇

贺亚峰,刘富成,范伟丽,董丽芳

收稿日期:2011-07-24 修回日期:2011-08-18 出版日期:2012-02-15 发布日期:2012-02-15
通讯作者: 董丽芳,Donglf@hbu.edu.cn E-mail:Donglf@hbu.edu.cn

Controlling the transition between Turing and antispiral patterns by using time-delayed-feedback

He Ya-Feng(贺亚峰), Liu Fu-Cheng(刘富成), Fan Wei-Li(范伟丽), and Dong Li-Fang(董丽芳)^†

Hebei Key Laboratory of Optic-electronic Information Materials, College of Physical Science and Technology, Hebei University, Baoding 071002, China

Received:2011-07-24 Revised:2011-08-18 Online:2012-02-15 Published:2012-02-15
Contact: Dong Li-Fang,Donglf@hbu.edu.cn E-mail:Donglf@hbu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 10975043 and 10947166), the Natural Science Foundation of Hebei Province, China (Grant Nos. A2011201006 and A2010000185), and the Science Foundation of Hebei University.

摘要/Abstract

Abstract: The controllable transition between Turing and antispiral patterns is studied by using a time-delayed-feedback strategy in a FitzHugh-Nagumo model. We treat the time delay as a perturbation and analyse the effect of the time delay on the Turing and Hopf instabilities near the Turing-Hopf codimension-two phase space. Numerical simulations show that the transition between the Turing patterns (hexagon, stripe, and honeycomb), the dual-mode antispiral, and the antispiral by applying appropriate feedback parameters. The dual-mode antispiral pattern originates from the competition between the Turing and Hopf instabilities. Our results have shown the flexibility of the time delay on controlling the pattern formations near the Turing-Hopf codimension-two phase space.

Key words: pattern formation, Turing-Hopf bifurcations, time delay

中图分类号: (Pattern selection; pattern formation)

47.54.-r

82.40.Ck (Pattern formation in reactions with diffusion, flow and heat transfer) 82.40.Bj (Oscillations, chaos, and bifurcations)

贺亚峰,刘富成,范伟丽,董丽芳. [J]. 中国物理B, 2012, 21(3): 34701-034701.

He Ya-Feng(贺亚峰), Liu Fu-Cheng(刘富成), Fan Wei-Li(范伟丽), and Dong Li-Fang(董丽芳) . Controlling the transition between Turing and antispiral patterns by using time-delayed-feedback[J]. Chin. Phys. B, 2012, 21(3): 34701-034701.

参考文献

[1] Cross C C and Hohenberg P C 1993 Rev. Mod. Phys. 65 851
[2] Ouyang Q and Swinney H L 1991 Nature 352 610
[3] Zaikin A N and Zhabotinsky A M 1970 Nature 225 535
[4] Guo W Q, Qiao C, Zhang Z M, Ouyang Q and Wang H L 2010 Phys. Rev. E 81 056214
[5] Mikhailov A S and Showalter K 2006 Phys. Rep. 425 79
[6] Luo J M and Zhan M 2010 Phys. Rev. E 78 016214
[7] Chen J X, Xu J R, Yuan X P and Ying H P 2009 J. Phys. Chem. B 113 849
[8] Zhang H, Cao Z J, Wu N J, Ying H P and Hu G 2005 it Phys. Rev. Lett. 94 188301
[9] Cui X H, Huang X Q, Cao Z J, Zhang H and Hu G 2008 it Phys. Rev. E 78 026202
[10] Tang G N, Deng M Y, Hu B and Hu G 2008 Phys. Rev. E 77 046217
[11] Ma J, Jia Y, Yi M, Tang J and Xia Y F 2009 Chaos, Solitons Fractals 41 1331
[12] Schneider F M, Schöll E and Dahlem M A 2009 Chaos 19 015110
[13] Kheowan O U, Zykov V S and M黮ler S C 2002 Phys. Chem. Chem. Phys. 4 1334
[14] He Y F, Ai B Q and Hu B B 2010 J. Chem. Phys. 133 114507
[15] Hu H X, Li Q S and Li S 2007 Chem. Phys. Lett. 447 364
[16] Golovin A A, Kanevsky Y and Nepomnyashchy A A 2009 Phys. Rev. E 79 046218
[17] Wang W M, Liu H Y, Cai Y L and Li Z Q 2011 Chin. Phys. B 20 074702
[18] Li H H, Xiao J H, Hu G and Hu B B 2010 Chin. Phys. B 19 050516
[19] Gotoh H, Kamada H, Saitoh T, Shigemori S and Temmyo J 2004 Appl. Phys. Lett. 85 2836
[20] Li Q S and Ji L 2004 Phys. Rev. E 69 046205
[21] Yang L F, Dolnik M, Zhabotinsky A M and Epstein I R 2002 Phys. Rev. Lett. 88 208303
[22] Ricard M R and Mischler S 2009 J. Nonlinear Sci. 19 1432
[23] Yang L F, Zhabotinsky A M and Epstein I R 2004 Phys. Rev. Lett. 92 198303
[24] Mau Y, Hagberg A and Meron E 2009 Phys. Rev. E 80 065203(R)
[25] de Kepper P, Perraud J J, Rudovics B and Dulos E 1994 it Int. J. Bifurcation and Chaos 4 1215
[26] Yuan X J, Shao X, Liao H M and Ouyang Q 2009 Chin. Phys. Lett. 26 024702

Controlling the transition between Turing and antispiral patterns by using time-delayed-feedback

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 13

Metrics

本文评价

推荐阅读 0

[1]	Jian Gao(高见), Changgui Gu(顾长贵), and Huijie Yang(杨会杰). Applying a global pulse disturbance to eliminate spiral waves in models of cardiac muscle[J]. 中国物理B, 2021, 30(7): 70501-070501.
[2]	韩蓉, 董丽芳, 黄加玉, 孙浩洋, 刘彬彬, 米彦霖. Influence of vibration on spatiotemporal structure of the pattern in dielectric barrier discharge[J]. 中国物理B, 2019, 28(7): 75204-075204.
[3]	冯帆, 闫佳, 刘富成, 贺亚峰. Pattern formation in superdiffusion Oregonator model[J]. 中国物理B, 2016, 25(10): 104702-104702.
[4]	李新政, 白占国, 李燕, 贺亚峰, 赵昆. Numerical simulation and analysis of complex patterns in a two-layer coupled reaction diffusion system[J]. , 2015, 24(4): 48201-048201.
[5]	王慧娟, 王永杰, 任芝. Control of the patterns by using time-delayed feedback near the codimension-three Turing–Hopf–Wave bifurcations[J]. Chin. Phys. B, 2013, 22(12): 120503-120503.
[6]	吴宁杰, 高洪俊, 应和平. Feedback control of wave segments in excitable medium[J]. 中国物理B, 2013, 22(5): 50501-050501.
[7]	范伟丽, 董丽芳. Spontaneous transition of one-dimensional plasma photonic crystal's orientation in dielectric barrier discharge[J]. Chin. Phys. B, 2013, 22(1): 14213-014213.
[8]	王玮明, 刘厚业, 蔡永丽, 李镇清. Turing pattern selection in a reaction–diffusion epidemic model[J]. 中国物理B, 2011, 20(7): 74702-074702.
[9]	袁国勇. Spiral-wave dynamics in excitable medium with excitability modulated by rectangle wave[J]. 中国物理B, 2011, 20(4): 40503-040503.
[10]	王玮明, 王文娟, 林晔智, 谭永基. Pattern selection in a predation model with self and cross diffusion[J]. 中国物理B, 2011, 20(3): 34702-034702.
[11]	高加振, 杨舒心, 谢玲玲, 高继华. Synchronizing spiral waves in a coupled Rössler system[J]. 中国物理B, 2011, 20(3): 30505-030505.
[12]	高忠科, 金宁德. Complex network analysis in inclined oil--water two-phase flow[J]. 中国物理B, 2009, 18(12): 5249-5258.
[13]	李国栋, 黄永念. Different localized states of travelling-wave convection in a rectangular container[J]. 中国物理B, 2006, 15(12): 2984-2988.