Adaptive synchronization control of coupled chaotic neurons in the external electrical stimulation

doi:10.1088/1674-1056/22/5/058701

中国物理B ›› 2013, Vol. 22 ›› Issue (5): 58701-058701.doi: 10.1088/1674-1056/22/5/058701

• INTERDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY • 上一篇下一篇

Adaptive synchronization control of coupled chaotic neurons in the external electrical stimulation

于海涛, 王江, 邓斌, 魏熙乐, 陈颖源

School of Electrical Engineering and Automation, Tianjin University, Tianjin 300072, China

收稿日期:2012-09-26 修回日期:2012-11-04 出版日期:2013-04-01 发布日期:2013-04-01
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 61072012, 61104032, and 61172009), and the Young Scientists Fund of the National Natural Science Foundation of China (Grant Nos. 60901035 and 50907044).

Adaptive synchronization control of coupled chaotic neurons in the external electrical stimulation

Yu Hai-Tao (于海涛), Wang Jiang (王江), Deng Bin (邓斌), Wei Xi-Le (魏熙乐), Chen Ying-Yuan (陈颖源)

School of Electrical Engineering and Automation, Tianjin University, Tianjin 300072, China

Received:2012-09-26 Revised:2012-11-04 Online:2013-04-01 Published:2013-04-01
Contact: Wang Jiang E-mail:jiangwang@tju.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 61072012, 61104032, and 61172009), and the Young Scientists Fund of the National Natural Science Foundation of China (Grant Nos. 60901035 and 50907044).

摘要/Abstract

摘要： In this paper we present a combined algorithm for the synchronization control of two gap junction coupled chaotic FitzHugh-Nagumo (FHN) neurons in the external electrical stimulation. The controller consists of a combination of dynamical sliding mode control and adaptive backstepping control. The combined algorithm yields an adaptive dynamical sliding mode control law which has advantages over static sliding mode-based controller of chattering-free, i.e., a sufficiently smooth control input signal is generated. It is shown that the proposed control scheme can not only compensate for the system uncertainty, but also guarantee the stability of the synchronized error system. In addition, numerical simulations are also performed to demonstrate the effectiveness of the proposed adaptive controller.

关键词: FitzHugh-Nagumo neuron, synchronization, adaptive control

Abstract: In this paper we present a combined algorithm for the synchronization control of two gap junction coupled chaotic FitzHugh-Nagumo (FHN) neurons in the external electrical stimulation. The controller consists of a combination of dynamical sliding mode control and adaptive backstepping control. The combined algorithm yields an adaptive dynamical sliding mode control law which has advantages over static sliding mode-based controller of chattering-free, i.e., a sufficiently smooth control input signal is generated. It is shown that the proposed control scheme can not only compensate for the system uncertainty, but also guarantee the stability of the synchronized error system. In addition, numerical simulations are also performed to demonstrate the effectiveness of the proposed adaptive controller.

Key words: FitzHugh-Nagumo neuron, synchronization, adaptive control

中图分类号: (Synchronization in the nervous system)

87.19.lm

于海涛, 王江, 邓斌, 魏熙乐, 陈颖源. Adaptive synchronization control of coupled chaotic neurons in the external electrical stimulation[J]. 中国物理B, 2013, 22(5): 58701-058701.

Yu Hai-Tao (于海涛), Wang Jiang (王江), Deng Bin (邓斌), Wei Xi-Le (魏熙乐), Chen Ying-Yuan (陈颖源). Adaptive synchronization control of coupled chaotic neurons in the external electrical stimulation[J]. Chin. Phys. B, 2013, 22(5): 58701-058701.

参考文献 30

[1]	Pikovsky A, Rosenblum M and Kurths J 2001 Synchronization: a Universal Concept in Nonlinear Sciences (Cambridge: Cambridge University Press)
[2]	Rabinovich M I, Varona P, Selverston A I and Abarbanel H D I 2006 Rev. Mod. Phys. 78 1213
[3]	Manyakov N V and van Hulle M M 2008 Chaos 18 037130
[4]	Elson R C, Selverston A I, Huerta R, Rulkov N F, Rabinovich M I and Abarbanel H D I 1998 Phys. Rev. Lett. 81 5692
[5]	Boccaletti S, Kurths J, Osipov G, Valladares D L and Zhou C S 2002 Phys. Rep. 366 1
[6]	Singer W 1993 Annu. Rev. Physiol. 55 349
[7]	MacKay W A 1997 Trends Cogn. Sci. 1 176
[8]	Levy R, Hutchison W D, Lozano A M and Dostrovsky J O 2000 J. Neurosci. 20 7766
[9]	Albert W W, Wright E J and Feinstein B 1969 Nature 221 670
[10]	Milton J and Jung P 2003 Epilepsy as a Dynamic Disease (Berlin: Springer-Verlag)
[11]	Li Z and Han C Z 2002 Chin. Phys. 11 9
[12]	Li G H, Zhou S P and Xu D M 2004 Chin. Phys. 13 168
[13]	Yu Y G and Zhang S C 2002 Chin. Phys. 11 1249
[14]	Zheng Z G, Hu G, Zhou C S and Hu B B 2000 Acta Phys. Sin. 49 2320 (in Chinese)
[15]	Huang X G, Xu J X, Huang W and Lü Z J 2001 Chin. Phys. 10 1113
[16]	Wang J, Deng B and Tsang K M 2004 Chaos Soliton. Fract. 22 469
[17]	Wang Q Y, Lu Q S, Chen G R and Guo D H 2006 Phys. Lett. A 356 17
[18]	Che Y Q, Wang J, Zhou S S and Deng B 2009 Chaos Soliton. Fract. 40 1333
[19]	Che Y Q, Wang J, Cui S G, Deng B, Wei X L, Chan W L and Tsang K M 2011 Nonlinear Analysis: Real World Applications 12 3199
[20]	Wang J, Deng B and Fei X Y 2006 Chaos Soliton. Fract. 29 182
[21]	Wang J, Deng B and Fei X Y 2006 Chaos Soliton. Fract. 27 1272
[22]	Batista C A S, Lopes S R, Viana R L and Batista A M 2010 Neural Netw. 23 114
[23]	Popovych O V, Hauptmann C and Tass P A 2006 Biol. Cybernet. 95 69
[24]	FitzHugh R 1961 Biophys. J. 1 445
[25]	Thompson C J, Bardos D C, Yang Y S and Joyner K H 1999 Chaos Soliton. Fract. 10 1825
[26]	Sira-Ramirez H 1992 Int. J. Control 56 1
[27]	Lü L, Yu M, Wei L L, Zhang M and Li Y S 2012 Chin. Phys. B 21 100507
[28]	Zhou J and Wen C 2008 Adaptive Backstepping Control of Uncertain Systems: Nonsmooth Nonlinearities, Interactions or Time-Variations (Heidelberg, Berlin: Springer-Verlag)
[29]	Rolf V and Robert W 2002 Biol. Cell. 94 501
[30]	Stephen B 2003 Biosystems 68 213

Adaptive synchronization control of coupled chaotic neurons in the external electrical stimulation

Adaptive synchronization control of coupled chaotic neurons in the external electrical stimulation

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