Optimization of self-adaptive synchronization and parameters estimation in chaotic Hindmarsh-Rose neuron model

Ma Jun; Su Wen-Tao; Gao Jia-Zhen

doi:10.7498/aps.59.1554

Abstract

Optimization of self-adaptive synchronization is investigated to estimate a group of five unknown parameters in one certain chaotic neuron model, which is described by the Hindmarsh-Rose. Two controllable gain coefficients are introduced into the Lyapunov function, which is necessary to get the form of parameter observers and controllers for parameter estimation and synchronization, to adjust the transient period for complete synchronization and parameter identification. It is found that the identified results for the minimal parameter （three orders of magnitude less than the maximal parameter） oscillate with time （the estimated results for this parameter is not exact） while the four remaining parameters are estimated very well when one controller and five parameter observers are used to work on the driven system （response system）. To the best of our knowledge, it could result from the great difference of five target parameters （values）. As a result, this problem could be solved when two controllers and five parameter observers are used to change the driven system and all the unknown parameters are identified with high precision. Furthermore, longer transient period for parameter estimation and complete synchronization is required when too strong gain coefficients are used, whils parameters can not be estimated exactly if too weak gain coefficients are used. Therefore, appropriate gain coefficients are critical to achieve the shortest transient period for parameter identification and complete synchronization of chaotic systems, and the optimization of gain coefficients depends on the model being studied. Furthermore, it is confirmed by our numerical results that this scheme is effective and reliable to estimate the parameters even if some parameters jump suddenly.

Keywords:

Authors and contacts

1.
兰州理工大学物理系,兰州 730050

References

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Cited By

[1]	［1］Boccaletti S, Grebogi C, Lai Y C, Mancini H, Maza D 2000 Phys. Rep. 329 103
[2]	［2］Boccaletti S, Kurths J, Osipov G, Valladares D L, Zhou C S 2002 Phys. Rep. 366 1
[3]	［3］Chen S H, Zhao L M , Liu Jie 2002 Chin. Phys. 11 543
[4]	［4］Yu S M ,Ma Z G ,Qiu S S, Peng S G, Lin Q H 2004 Chin. Phys.13 317
[5]	［5］Wang Q Yun, Lu Q S , Wang H X 2005 Chin. Phys. 14 2189
[6]	［6］Zou Y L, Zhu J,Chen G R 2005 Chin. Phys . 14 697
[7]	［7］Lü L , Zhang Q L,Guo Z A 2008 Chin. Phys. B 17 498
[8]	［8］Wei D Q , Luo X S 2007 Chin. Phys. 16 3244
[9]	［9］Wei D Q , Luo X S 2008 Chin. Phys. B 17 92
[10]	］Wang F Q ,Liu C X 2007 Chin. Phys. 16 946
[11]	］Ma J, Jin W Y , Li Y L 2008 Chaos,Solitons & Fractals 36 494
[12]	］Wang Q Y, Jin W Y, Xia Y F 2008 Chin. Phys. Lett. 25 3582
[13]	］Li Z, Han C Z 2002 Chin. Phys. 11 9
[14]	］Xiao Y Z,Xu W 2007 Chin. Phys. 16 1597
[15]	］Lü L,Guo Z A ,Zhang C 2007 Chin. Phys. 16 1603
[16]	］Xiao Y Z, Xu W, Li X C, Tang S F 2008 Chin. Phys. B 17 80
[17]	］Liu Z R, Luo J G 2006 Chin. Phys. Lett. 23 1118
[18]	］Wang H X, Lu Q S, Wang Q Y 2005 Chin. Phys. Lett. 22 2173
[19]	］Yang X L, Xu W 2008 Chin. Phys. B 17 2004
[20]	］Li X W, Zheng Z G 2007 Commun. Theor. Phys. 47 265
[21]	］Shi X , Lu Q S 2005 Chin. Phys. Lett. 22 547
[22]	］Zhan M, Hu G ,Wang X G 2000 Chin. Phys. Lett. 17 332
[23]	］Ho M C, Hung Y C ,Chou C H 2002 Phys. Lett. A 296 43
[24]	］Shuai J W, Durand D M 1999 Phys. Lett. A 264 289
[25]	］Vincent U E, Njah A N , Solarin A R T 2006 Physica A 360 186
[26]	］Li G H 2007 Chin. Phys. 16 2608
[27]	］Li D , Zheng Z G 2008 Chin. Phys. B 17 4009
[28]	］Yang J Z , Hu G 2007 Phys. Lett. A 361 332
[29]	］Yang J Z, Zhang M 2008 Commun. Theor. Phys. 49 391
[30]	］Min L Q, Chen G R, Zhang X D, Zhang X H, Yang M 2004 Commun. Theor. Phys. 41 632
[31]	］Jing J Y, Min L Q 2009 Chin. Phys. Lett. 26 028702
[32]	］Chen Y H, Wu Z Y, Yang J Z 2007 Chin. Phys. Lett. 24 46
[33]	］Li C D , Liao X F 2004 Phys. Lett. A 329 301
[34]	］Shahverdiev E M , Shore K A Phys. Lett. A 292 320
[35]	］Zhang H G, Ma T D,Yu W , Fu J 2008 Chin. Phys. B 17 3616
[36]	］Gao J, Zheng Z G, He D Hi, Zhang T X 2003 Chin. Phys. Lett. 20 999
[37]	］Mu J, Tao C , Du G H 2003 Chin. Phys. 12 381
[38]	］Wu L , Zhu S Q 2003 Chin. Phys. 12 300
[39]	］Lu J G , Xi Y G 2005 Chin. Phys. 14 274
[40]	］Xu J F, Min L Q , Chen G R 2004 Chin. Phys. Lett. 21 1445
[41]	］Shi X , Lu Q S 2005 Chin. Phys.14 77
[42]	］Hindmarsh J L , Rose R M 1982 Nature 276 162
[43]	］Hindmarsh J L , Rose R M 1984 Proc. R. Soc. Lond. B 221 87
[44]	］Gao B J ,Lu J A 2007 Chin. Phys.16 666
[45]	］Cai G L, Zheng S , Tian L X 2008 Chin. Phys. B 17 2412
[46]	］Huang J 2008 Phys. Lett. A 372 4799
[47]	］Wang Y W,Wen C Y, Yang M , Xiao J W 2008 Phys. Lett. A 372 2409
[48]	］Zhang G, Liu Z R , Zhang J B 2008 Phys. Lett. A 372 447
[49]	］Elabbasy E M, El-Dessoky M M 2006 Phys. Lett. A 349 187
[50]	］Li L, Li J F, Liu Y P, Ma J, 2008 Acta Phys. Sin. 57 1404（in Chinese）［李农、李建芬、刘宇平、马健 2008 物理学报 57 1404］
[51]	］Li L, Li J F, Cai L , Zhang B, 2008 Acta Phys. Sin. 57 7500（in Chinese）［李农、李建芬、蔡理、张斌 2008 物理学报 57 7500］

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Vol. 59, Issue 3 - 2010-02-05

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