一类新的混沌神经放电的动力学特征的实验和数学模型研究

古华光; 朱洲; 贾冰

doi:10.7498/aps.60.100505

摘要

神经元电活动理论模型Hindmarsh-Rose(HR)模型提示有位于周期1和周期2放电模式之间的一类特殊的混沌放电,但长期以来对其没有获得足够认识.依据回归映射的确定性结构和非线性预报的短期可预报性,确认了在大鼠的实验性神经起步点的实验中发现的位于周期1和周期2放电模式之间的非周期放电是混沌放电模式,还将该混沌放电模式区分为3个不同表观样式.其中1个表观形式与HR模型的仿真结果相类似,验证了HR模型的理论预期;其余2个样式与仿真结果并不相似.进一步揭示了3个表观样式的动力学特征以及相互之间的区别与联系,并与位于周期2和周期3节律之间、周期3和周期4节律之间的混沌比较了异同,也区别了从周期1到混沌再到周期2放电模式的节律转迁历程与其他的从周期1到周期2节律的分岔过程的不同.研究结果确认了该类特殊混沌节律和相应分岔过程的新特征,丰富了混沌放电节律和节律分岔序列的种类.还对仿真该混沌的多样性和非光滑特性,以及揭示该类混沌的产生途径等进行了讨论.

关键词:

混沌 /
神经放电模式 /
分岔 /
节律

Abstract

A special chaotic firing pattern lying between period-1 and period-2 firing pattern simulated in theoretical neuronal firing model, Hindmarsh-Rose (HR) model, has not been adequately understood for a long time. The non-periodic neural firing patterns lying between period-1 and period-2 firing pattern discovered in the biological experiments on neural pacemakers of rats are identified to be chaotic bursting and divided into three styles in appearance, according to the deterministic structures of the first return map and the short-term predictability of nonlinear predication. One style of the experimental chaos exhibits characteristics similar to the numerical simulations of the theoretical model, verifying the theoretical participation of HR model, while other styles display different characteristics. The characteristics of the three styles and the relationship and distinction among 3 styles of the chaotic rhythms are identified, and compared with those lying between period-2 and period-3 firing pattern, and between period-3 and period-4 firing pattern. In addition, the distinction between the transition procedure from period-1 to chaos and then to period-2 and other bifurcation scenarios from period-1 to period-2 firing pattern is also identified. The results confirm the novel chaos lying between period-1 and period-2 and the corresponding novel bifurcation scenario, enriching the kinds of the chaotic rhythms and bifurcation scenarios of neural firing. Finally simulations of the diversity and non-smooth characteristics of the chaotic rhythms discovered in the experiment and identification of the routine to chaos are also discussed.

Keywords:

作者及机构信息

1.
陕西师范大学生命科学学院,西安 710062

基金项目: 国家自然科学基金(批准号:11072135, 10772101)和中央高校基本科研业务费基金(批准号:GK200902025)资助的课题.

Authors and contacts

1.
College of Life Science, Shaanxi Normal University, Xi’an 710062, China

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施引文献

[1]	Garfinkel A, Spano M L, Ditto W L 1992 Science 257 1230
[2]
[3]	Schiff S J, Jerger K, Duong D H 1994 Nature 370 615
[4]
[5]	He G G, Zhu P, Chen H P, Xie X P 2010 Acta Phys. Sin. 59 5307(in Chinese) [何国光、朱萍、陈宏平、谢小平 2010 物理学报 59 5307].
[6]	Wang Z S, Zhang H G, Wang Z L 2006 Acta Phys. Sin. 55 2687 (in Chinese)[王占山、张化光、王智良 2006 物理学报 55 2687]
[7]
[8]	Gu H G, Yang M H, Li L, Ren W, Lu Q S 2007 Dyn. Continuous Discrete Impulsive Syst. (Ser. B Appl. Algorithms) 14 6
[9]
[10]	Lu Q S, Gu H G, Yang Z Q, Duan L X, Shi X, Zheng Y H 2008 Acta Mech. Sin. 24 593
[11]
[12]
[13]	Wu X B, Mo J, Yang M H, Zheng Q H, Gu H G, Ren W 2008 Chin. Phys. Lett. 25 2799
[14]	Yang M H, Liu Z Q, Li L, Xu Y L, Liu H J, Gu H G, Ren W 2009 Int. J. Bif. Chaos 19 453
[15]
[16]	Lu Q S, Yang Z Q, Duan L X, Gu H G, Ren W 2009 Chaos Solitons Fractals 40 577
[17]
[18]
[19]	Wang D, Mo J, Zhao X Y, Gu H G, Qu S X, Ren W 2010 Chin. Phys. Lett. 27 070503
[20]
[21]	Thomas E, William J R, Zbigniew J K, James E S, Karl E G, Niels B 1994 Physiol. Rev. 74 1
[22]
[23]	Lovejoy L P, Shepard P D, Canavier C C 2001 Neuroscience 104 829
[24]
[25]	Quyen M L V, Martinerie M J, Adam C, Varela F J 1997 Phys. Rev. E 56 3401
[26]
[27]	Pei X, Moss F 1996 Nature 379 618
[28]	Kanno T, Miyano T, Tokudac I, Galvanovskisd J, Wakui M 2007 Physica D 226 107
[29]
[30]	So P, Francis J T, Netoff T I, Gluckma B J, Schiff S J 1998 Biophys. J. 74 2776
[31]
[32]	Rabinovich M I, Abarbanel H D I 1998 Neuroscience 87 5
[33]
[34]	Schweighofer N, Doya K, Fukai H, Chiron J V, Furukawa T, Kawato M 2004 Proc. Natl. Acad. Sci. USA 101 4655
[35]
[36]	Hu S J, Yang H J, Jian Z, Long K P, Duan Y B, Wan Y H, Xing J L, Xu H, Ju G 2000 Neuroscience 101 689
[37]
[38]
[39]	Hayashi H, Ishzuka S, Ohta M, Hirakawa K 1982 Phys. Lett. A 88 435
[40]	Hayashi H, Ishzuka S, Hirakawa K 1983 Phys. Lett. A 98 474
[41]
[42]
[43]	Aihara K, Matsumoto G, Ikegaya Y 1984 J. Theor. Biol. 109 249
[44]
[45]	Fan Y S, Holden A V 1993 Chaos Solitons Fractals 3 439
[46]	Chay T R 1985 Physica D 16 233
[47]
[48]
[49]	Ren W, Hu S J, Zhang B J, Xu J X, Gong Y F 1997 Int. J. Bif. Chaos. 7 1867
[50]	Duan Y B, Jian Z, Hu S J, Ren W 1998 Acta Biophys. Sin. 14 466(In Chinese) [段玉斌、菅忠、胡三觉、任维 1998 生物物理学报 14 466]
[51]
[52]	Xu J X, Gong Y F, Ren W, Hu S J, Wang F Z 1997 Physica D 100 212
[53]
[54]	Gong Y F, Xu J X, Ren W, Hu S J, Wang F Z 1998 Biol. Cybern.78 159
[55]
[56]	Ren W, Gu H G, Jian Z, Lu Q S, Yang M H 2001 NeuroReport 12 2121
[57]
[58]
[59]	Xie Y, Xu J X, Kang Y M, Hu S J, Duan Y B 2003 Acta Phys. Sin. 52 1112 (in Chinese)[谢勇、徐健学、康艳梅、胡三觉、段玉斌 2003 物理学报 52 1112]
[60]
[61]	Li L, Gu H G, Yang M H, Liu Z Q, Ren W 2004 Int. J. Bif. Chaos 14 1813
[62]
[63]	Gu H G, Yang M H, Li L, Liu Z Q, Ren W 2004 Dyn. Continuous Discrete Impulsive Syst. (Ser. B Appl. Algorithms) 11 19
[64]
[65]	Gong P L, Xu J X, Hu S J, Long K P 2002 Int. J. Bif. Chaos 12 319
[66]	Jian Z, Xing J L, Yang G S, Hu S J 2004 NeuroSignals 13 150
[67]
[68]
[69]	Wan Y H, Jian Z, Hu S J 2000 NeuroReport 11 3295
[70]
[71]	Huber M T, Krige J C, Braun H A, Pei X, Neiman A, Moss F 2000 Neurocomputing 32-33 823
[72]	Wu S G, He D R 2001 J. Phys. Soc. Jpn. 70 69
[73]
[74]	Wu S G, He D R 2000 Chin. Phys. Lett.17 398
[75]
[76]
[77]	Wu S G, He D R 2001 Commun. Theor. Phys. 35 272
[78]
[79]	Wang Y M, Wang X M, Chen H S, Wan W X, Zhao J G, He D R 2002 Acta Phys. Sin. 51 1457 (in Chinese)[汪颖梅、王旭明、陈贺胜、王文秀、赵金刚、何大韧 2002 物理学报 51 1475]
[80]
[81]	Braun H A, Wissing H, Schfer K, Hirsch M C 1994 Nature 367 270
[82]
[83]	Yang M H, An S C, Gu H G, Liu Z Q, Ren W 2006 Neuro. Report 17 995
[84]	Gu H G, Yang M H, Li L, Liu Z Q, Ren W 2003 Phys. Lett. A 319 89
[85]
[86]	Sauer T 1994 Phys. Rev. Lett. 72 3811
[87]
[88]
[89]	Theiler J, Eubank S, Longtin A, Galdrinkian B 1992 Physica D 58 77
[90]
[91]	Xu Y L, Li L, Yang M H, Liu Z Q, Liu H J, Gu H G, Ren W 2007 Dyn. Continuous Discrete Impulsive Syst. (Ser. B Appl. Algorithms) 14 41
[92]
[93]	Medvedev G S 2005 Physica D 202 37
[94]
[95]	Mo J, Li Y Y, Wei C L, Yang M H, Liu Z Q, Gu H G, Qu S X, Ren W 2010 Chin. Phys. B 19 080513

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