Hindmarsh-Rose混沌神经元自适应同步和参数识别的优化研究

马军; 苏文涛; 高加振

doi:10.7498/aps.59.1554

摘要

以Hindmarsh-Rose混沌神经元模型为例，讨论了基于自适应同步识别混沌系统多个参数方法的优化问题. 在构造的李亚普诺夫函数中引入可调节的增益系数来控制系统同步和参数观测器的暂态过程长短. 在应用单个控制器和5个参数观测器来同步和识别Hindmarsh-Rose混沌神经元中5个未知参数时发现最小参数的识别结果出现了振荡而其他参数都能准确识别现象，分析其原因可能在于要识别的目标参数的巨大差异性. 通过增加控制器的个数（选择两个控制器）可以克服这个困难. 研究发现增益系数太小不能实现完全同步和参数的准确

关键词:

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:

作者及机构信息

1.
兰州理工大学物理系,兰州 730050

基金项目: 国家自然科学基金（批准号：10747005, 30670529）和兰州理工大学青年基金（批准号：Q200706）资助的课题.

Authors and contacts

1.
兰州理工大学物理系,兰州 730050

参考文献

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施引文献

[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 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 57 7500］

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