Please wait a minute...
Chin. Phys. B, 2012, Vol. 21(3): 034701    DOI: 10.1088/1674-1056/21/3/034701
ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS Prev   Next  

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
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.
Keywords:  pattern formation      Turing-Hopf bifurcations      time delay  
Received:  24 July 2011      Revised:  18 August 2011      Accepted manuscript online: 
PACS:  47.54.-r (Pattern selection; pattern formation)  
  82.40.Ck (Pattern formation in reactions with diffusion, flow and heat transfer)  
  82.40.Bj (Oscillations, chaos, and bifurcations)  
Fund: 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.
Corresponding Authors:  Dong Li-Fang,Donglf@hbu.edu.cn     E-mail:  Donglf@hbu.edu.cn

Cite this article: 

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 2012 Chin. Phys. B 21 034701

[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
[1] Hopf bifurcation and phase synchronization in memristor-coupled Hindmarsh-Rose and FitzHugh-Nagumo neurons with two time delays
Zhan-Hong Guo(郭展宏), Zhi-Jun Li(李志军), Meng-Jiao Wang(王梦蛟), and Ming-Lin Ma(马铭磷). Chin. Phys. B, 2023, 32(3): 038701.
[2] Effect of autaptic delay signal on spike-timing precision of single neuron
Xuan Ma(马璇), Yaya Zhao(赵鸭鸭), Yafeng Wang(王亚峰), Yueling Chen(陈月玲), and Hengtong Wang(王恒通). Chin. Phys. B, 2023, 32(3): 038703.
[3] Review on typical applications and computational optimizations based on semiclassical methods in strong-field physics
Xun-Qin Huo(火勋琴), Wei-Feng Yang(杨玮枫), Wen-Hui Dong(董文卉), Fa-Cheng Jin(金发成), Xi-Wang Liu(刘希望), Hong-Dan Zhang(张宏丹), and Xiao-Hong Song(宋晓红). Chin. Phys. B, 2022, 31(3): 033101.
[4] Inferring interactions of time-delayed dynamic networks by random state variable resetting
Changbao Deng(邓长宝), Weinuo Jiang(蒋未诺), and Shihong Wang(王世红). Chin. Phys. B, 2022, 31(3): 030502.
[5] Bifurcation and dynamics in double-delayed Chua circuits with periodic perturbation
Wenjie Yang(杨文杰). Chin. Phys. B, 2022, 31(2): 020201.
[6] Finite-time Mittag—Leffler synchronization of fractional-order complex-valued memristive neural networks with time delay
Guan Wang(王冠), Zhixia Ding(丁芝侠), Sai Li(李赛), Le Yang(杨乐), and Rui Jiao(焦睿). Chin. Phys. B, 2022, 31(10): 100201.
[7] Phase-field study of spinodal decomposition under effect of grain boundary
Ying-Yuan Deng(邓英远), Can Guo(郭灿), Jin-Cheng Wang(王锦程), Qian Liu(刘倩), Yu-Ping Zhao(赵玉平), and Qing Yang(杨卿). Chin. Phys. B, 2021, 30(8): 088101.
[8] 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.
[9] Delayed excitatory self-feedback-induced negative responses of complex neuronal bursting patterns
Ben Cao(曹奔), Huaguang Gu(古华光), and Yuye Li(李玉叶). Chin. Phys. B, 2021, 30(5): 050502.
[10] Modeling and dynamics of double Hindmarsh-Rose neuron with memristor-based magnetic coupling and time delay
Guoyuan Qi(齐国元) and Zimou Wang(王子谋). Chin. Phys. B, 2021, 30(12): 120516.
[11] Stabilization strategy of a car-following model with multiple time delays of the drivers
Weilin Ren(任卫林), Rongjun Cheng(程荣军), and Hongxia Ge(葛红霞). Chin. Phys. B, 2021, 30(12): 120506.
[12] Multiple Lagrange stability and Lyapunov asymptotical stability of delayed fractional-order Cohen-Grossberg neural networks
Yu-Jiao Huang(黄玉娇), Xiao-Yan Yuan(袁孝焰), Xu-Hua Yang(杨旭华), Hai-Xia Long(龙海霞), Jie Xiao(肖杰). Chin. Phys. B, 2020, 29(2): 020703.
[13] Enhanced vibrational resonance in a single neuron with chemical autapse for signal detection
Zhiwei He(何志威), Chenggui Yao(姚成贵), Jianwei Shuai(帅建伟), and Tadashi Nakano. Chin. Phys. B, 2020, 29(12): 128702.
[14] Design of passive filters for time-delay neural networks with quantized output
Jing Han(韩静), Zhi Zhang(章枝), Xuefeng Zhang(张学锋), and Jianping Zhou(周建平). Chin. Phys. B, 2020, 29(11): 110201.
[15] Validity of extracting photoionization time delay from the first moment of streaking spectrogram
Chang-Li Wei(魏长立), Xi Zhao(赵曦). Chin. Phys. B, 2019, 28(1): 013201.
No Suggested Reading articles found!