Please wait a minute...
Chin. Phys. B, 2013, Vol. 22(5): 050501    DOI: 10.1088/1674-1056/22/5/050501
GENERAL Prev   Next  

Feedback control of wave segments in excitable medium

Wu Ning-Jiea, Gao Hong-Juna, Ying He-Pingb
a Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210046, China;
b Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 310027, China
Abstract  Depending on the excitability of the medium, a propagating wave segment would either contract or expend to fill the medium with spiral waves. This paper aims to introduce a simple mechanism of feedback control to stabilize such an expansion or contraction. To do this, we lay out a feedback control system in a block diagram and reduce it into a bare, universal formula. Analytical and experimental findings are compared through a series of numerical simulations of the Barkley model.
Keywords:  feedback control      wave segments      excitable medium  
Received:  07 September 2012      Revised:  05 November 2012      Published:  01 April 2013
PACS:  05.45.-a (Nonlinear dynamics and chaos)  
  05.65.+b (Self-organized systems)  
  47.54.-r (Pattern selection; pattern formation)  
  82.40.Bj (Oscillations, chaos, and bifurcations)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11105074 and 11005026), the Natural Science Foundation of the Higher Education Institutions of Jiangsu Province, China (Grant Nos. 11KJB140004 and 11KJA110001), and the Qing Lan Project of Jiangsu Province, China.
Corresponding Authors:  Wu Ning-Jie     E-mail:

Cite this article: 

Wu Ning-Jie, Gao Hong-Jun, Ying He-Ping Feedback control of wave segments in excitable medium 2013 Chin. Phys. B 22 050501

[1] Mikhailov A and Showalter K 2006 Phys. Rep. 425 79
[2] Winfree A T 1972 Science 175 634
[3] Zhabotinsky A M and Zaikin A N 1973 J. Theor. Bio. 40 45
[4] Winfree A T 1994 Science 266 1003
[5] Alonso S, Sagués F and Mikhailov A S 2003 Science 299 1722
[6] Ma J, Wang C N, Jin W Y and Wu Y 2010 Appl. Math. Comput. 217 3844
[7] Panfilov A V, Keldermann R H and Nash M P 2007 Proc. Natl. Acad. Sci. 104 7922
[8] Faridon A 2010 Appl. Math. Comput. 217 3385
[9] Henry H 2004 Phys. Rev. E 70 026204
[10] Lenka S, Elena S and Hana S 2005 Biophys. Chem. 113 269
[11] Zhang H, Bambi H and Hu G 2003 Phys. Rev. E 68 026134
[12] Zykov V S, Steinbock O and Muller S C 1994 Chaos 4 509
[13] Braune M, Schrader A and Engel H 1994 Chem. Phys. Lett. 222 358
[14] Jia X, Zhou L Q and Ouyang Q 2004 Chin. Phys. Lett. 21 435
[15] Franklin G, Powell J D and Emami-Naeini A 2005 Feedback Control of Dynamic Systems (5th edn.) (Prentice Hall)
[16] Luo X S, Gao Y, Wang B H, Feng J and Yuan G 2001 Chin. Phys. 10 17
[17] Schlesner J, Zykov V, Engel H and Schöll E 2006 Phys. Rev. E 74 046215
[18] Grill S, Zykov V S and Müller S C 1995 Phys. Rev. Lett. 75 3368
[19] Zykov V S and Engel H 2004 Physica D 199 243
[20] Guo W Q, Qiao C, Zhang Z M, Ouyang Q and Wang H L 2010 Phys. Rev. E 81 056214
[21] Schlesner J, Zykov V S, Brandtstädter H, Gerdes I and Engel H 2008 New J. Phys. 10 015003
[22] Wu N J, Gao H J and Ying H P 2010 Phys. Rev. E 82 066206
[23] Mihaliuk E, Sakurai T, Chirila F and Showalter K 2002 Faraday Discuss. 120 383
[24] Sakurai T, Osaki K and Tsujikawa T 2008 Physica D 237 3165
[25] Mihaliuk E, Sakurai T, Chirila F and Showalter K 2002 Phys. Rev. E 65 065602
[26] Zykov V S 2008 Eur. Phys. J. Spec. Top. 157 209
[27] Sakurai T and Osaki K 2008 Comm. Nonlinear. Sci. Num. Simu. 13 1067
[1] Influence of homodyne-based feedback control on the entropic uncertainty in open quantum system
Juju Hu(胡菊菊), Qin Xue(薛琴). Chin. Phys. B, 2019, 28(7): 070303.
[2] H couple-group consensus of stochastic multi-agent systems with fixed and Markovian switching communication topologies
Muyun Fang(方木云), Cancan Zhou(周灿灿), Xin Huang(黄鑫), Xiao Li(李晓), Jianping Zhou(周建平). Chin. Phys. B, 2019, 28(1): 010703.
[3] Coordinated chaos control of urban expressway based on synchronization of complex networks
Ming-bao Pang(庞明宝), Yu-man Huang(黄玉满). Chin. Phys. B, 2018, 27(11): 118902.
[4] Quantum speed limit time of a two-level atom under different quantum feedback control
Min Yu(余敏), Mao-Fa Fang(方卯发), Hong-Mei Zou(邹红梅). Chin. Phys. B, 2018, 27(1): 010303.
[5] Successive lag synchronization on dynamical networks with communication delay
Xin-Jian Zhang(张新建), Ai-Ju Wei(韦爱举), Ke-Zan Li(李科赞). Chin. Phys. B, 2016, 25(3): 038901.
[6] Dissipative preparation of a steady three-dimensional entangled state via quantum-jump-based feedback
Chen Li, Wang Hong-Fu, Zhang Shou. Chin. Phys. B, 2014, 23(3): 030301.
[7] A control method applied to mixed traffic flow for the coupled-map car-following model
Cheng Rong-Jun, Han Xiang-Lin, Lo Siu-Ming, Ge Hong-Xia. Chin. Phys. B, 2014, 23(3): 030507.
[8] An improved car-following model with consideration of the lateral effect and its feedback control research
Zheng Ya-Zhou, Zheng Peng-Jun, Ge Hong-Xia. Chin. Phys. B, 2014, 23(2): 020503.
[9] The effect of cellular aging on the dynamics of spiral waves
Deng Min-Yi, Chen Xi-Qiong, Tang Guo-Ning. Chin. Phys. B, 2014, 23(12): 120503.
[10] Chaotic dynamic behavior analysis and control for a financial risk system
Zhang Xiao-Dan, Liu Xiang-Dong, Zheng Yuan, Liu Cheng. Chin. Phys. B, 2013, 22(3): 030509.
[11] Feedback control and synchronization of Mandelbrot sets
Zhang Yong-Ping. Chin. Phys. B, 2013, 22(1): 010502.
[12] Pinning synchronization of time-varying delay coupled complex networks with time-varying delayed dynamical nodes
Wang Shu-Guo,Yao Hong-Xing. Chin. Phys. B, 2012, 21(5): 050508.
[13] Bifurcations and chaos control in discrete small-world networks
Li Ning, Sun Hai-Yi, Zhang Qing-Ling. Chin. Phys. B, 2012, 21(1): 010503.
[14] Modified coupled map car-following model and its delayed feedback control scheme
Ge Hong-Xia. Chin. Phys. B, 2011, 20(9): 090502.
[15] Adaptive stabilization of an incommensurate fractional order chaotic system via a single state controller
Zhang Ruo-Xun, Yang Shi-Ping. Chin. Phys. B, 2011, 20(11): 110506.
No Suggested Reading articles found!