一类位于加周期分岔中的貌似混沌的随机神经放电节律的识别

古华光; 惠磊; 贾冰

doi:10.7498/aps.61.080504

摘要

识别非周期神经放电节律是混沌还是随机一直是一个重要的科学问题. 在神经起步点实验中发现了一类介于周期k和周期k+1(k=1,2)节律之间非周期自发放电节律, 其行为是长串的周期k簇和周期k+1簇的交替. 确定性理论模型Chay模型展示出了周期k和周期k+1节律的共存行为. 噪声在共存区诱发出了与实验结果类似的非周期节律, 说明该类节律是噪声引起的两类簇的跃迁. 非线性预报及其回归映射揭示该节律具有确定性机理; 将两类簇分别转换为0和1得到一个二进制序列, 对该序列进行概率分析获得了两类簇跃迁的随机机理. 这不仅说明该节律是具有确定性结构的随机节律而不是混沌, 还为深入识别现实神经系统的混沌和随机节律提供了典型示例和有效方法.

关键词:

Abstract

To identify non-periodic neural rhythm to be chaos or stochasticity has been an important scientific thesis. A kind of non-periodic spontaneous firing pattern, whose behavior is transition between period-k burst in a string and period-k+1 burst in a string (k=1,2), lying between period-k bursting pattern and period-k+1 bursting pattern, is found in the experimental neural pacemaker. The deterministic structures of the firing are identified by nonlinear prediction and first return map of the interspike intervals (ISIs) series. The co-existence of the period-k bursting and period-k+1 bursting is manifested in the deterministic theoretical neuronal model, Chay model. Non-periodic firing patterns similar to the experimental observation are simulated in the co-existing parameter region, implying that the firing pattern is transition between two kinds of bursts induced by noise. A binary series can be acquired by transforming two kinds of bursts to symbols 0 and 1, respectively. The stochastic dynamics within the transitions between two kinds of bursts are detected by probability analysis on the binary series. It not only shows that the rhythm is stochastic firing with deterministic structures instead of chaos, but also provides the typical examples and effective methods to intensively identify the chaotic and stochastic firing patterns in a real nervous system.

Keywords:

作者及机构信息

1.
陕西师范大学物理学与信息技术学院, 西安 710062;

2.
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, 10432010, 30300107)和中央高等学校基本科研基金(批准号: GK200902025)资助的课题.

Authors and contacts

1.
College of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, China;

2.
College of Life Sciences, Shaanxi Normal University, Xi’an 710062, China

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11072135, 10772101, 10432010, 30300107) and the Fundamental Scientific Research Foundation for the Central Universities of China (Grant No. GK200902025).

参考文献

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[26]	Wan Y H, Jian Z, Hu S J 2000 Neuroreport 11 3295
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[29]	Xing J L, Hu S J, Xu H, Han S, Wan Y H 2001 Neuroreport 12 1311
[30]	Gu H G, Ren W, Lu Q S, Wu S G, Yang M H, Chen W J 2001 Phys. Lett. A 285 63
[31]	Gong P L, Xu J X, Hu S J, Long K P 2002 Int. J. Bifur. Chaos 12 319
[32]	Gu H G, Jia B, Lu Q S 2011 Cogn. Neurodyn. 5 87
[33]	Gu H G, Zhang H M, Wei C L, Yang M H, Liu Z Q, Ren W 2011 Int. J. Mod. Phys. B 25 3977
[34]	Jia B, Gu H G, Li Y Y 2011 Chin. Phys. Lett. 28 090507
[35]	Huber M T, Krige J C, Braun H A, Pei X, Neiman A, Moss F 2000 Neurocomputing 32---33 823
[36]	Gu H G, Yang M H, Li L, Liu Z Q, Ren W 2003 Phys. Lett. A 319 89
[37]	Gu H G, Yang M H, Li L, Liu Z Q, Ren W 2003 Int. J. Mod. Phys. B 17 4195
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[39]	Theiler J, Eubank S, Longtin A, Galdrinkian B 1992 Physica D 58 77
[40]	Sauer T 1994 Phys. Rev. Lett. 72 3811

施引文献

[1]	May R M 1976 Nature 261 459
[2]	Gammaitoni L, Hänggi P, Jung P, Marchesoni F 1998 Rev. Mod. Phys. 70 22
[3]	Hayashi H, Ishzuka S, Ohta M, Hirakawa K 1982 Phys. Lett. A 88 435
[4]	Hayashi H, Ishzuka S, Hirakawa K 1983 Phys. Lett. A 98 474
[5]	Aihara K, Matsumoto G, Ikegaya Y 1984 J. Theor. Biol. 109 249
[6]	Hayashi H, Ishzuka S 1992 J. Theor. Biol. 156 269
[7]	Li L, Gu H G, Yang M H, Liu Z Q, Ren W 2004 Int. J. Bifur. Chaos 14 1813
[8]	Wang D, Mo J, Zhao X Y, Gu H G, Qu S X, Ren W 2010 Chin. Phys. Lett. 27 070503
[9]	Gu H G, Zhu Z, Jia B 2011 Acta Phys. Sin. 60 100505 (in Chinese) [古华光, 朱洲, 贾冰 2011 60 100505]
[10]	Yang M H, Liu Z Q, Li L, Xu Y L, Liu H J, Gu H G, Ren W 2009 Int. J. Bifur. Chaos 19 453
[11]	Ren W, Hu S J, Zhang B J, Xu J X, Gong Y F 1997 Int. J. Bifur. Chaos. 7 1867
[12]	Gu H G, Yang M H, Li L, Liu Z Q, Ren W 2004 Dynam. Contin. Dis. B 11 19
[13]	Zhao X Y, Song S L, Wei C L, Gu H G, Ren W 2010 Acta Biophys. Sin. 26 61 (in Chinese) [赵小燕, 宋绍丽, 魏春玲, 古华光, 任维 2010 生物 26 61]
[14]	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 52 1112]
[15]	Fan Y S, Holden A V 1993 Chaos Solitons Fract. 3 439
[16]	Chay T R 1985 Physica D 16 233
[17]	Wu S G, He D R 2000 Chin. Phys. Lett. 76 398
[18]	Wu S G, He D R 2001 Commun. Theor. Phys. 35 272
[19]	Schiff S J, Jerger K, Duong D H 1994 Nature 370 615
[20]	Thomas E, William J R, Zbigniew J K, James E S, Karl E G, Niels B 1994 Physiol. Rev. 74 1
[21]	Lovejoy L P, Shepard P D, Canavier C C 2001 Neuroscience 104 829
[22]	Kanno T, Miyano T, Tokudac I, Galvanovskisd J, Wakui M 2007 Physica D 226 107
[23]	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
[24]	So P 1998 Biophys J. 74 2776
[25]	Jian Z, Xing J L, Yang G S, Hu S J 2004 Neurosignals 13 150
[26]	Wan Y H, Jian Z, Hu S J 2000 Neuroreport 11 3295
[27]	Longtin A, Bulsara A, Moss F 1991 Phys. Rev. Lett. 67 656
[28]	Braun H A, Wissing H, Schäfer K, Hirsch M C 1994 Nature 367 270
[29]	Xing J L, Hu S J, Xu H, Han S, Wan Y H 2001 Neuroreport 12 1311
[30]	Gu H G, Ren W, Lu Q S, Wu S G, Yang M H, Chen W J 2001 Phys. Lett. A 285 63
[31]	Gong P L, Xu J X, Hu S J, Long K P 2002 Int. J. Bifur. Chaos 12 319
[32]	Gu H G, Jia B, Lu Q S 2011 Cogn. Neurodyn. 5 87
[33]	Gu H G, Zhang H M, Wei C L, Yang M H, Liu Z Q, Ren W 2011 Int. J. Mod. Phys. B 25 3977
[34]	Jia B, Gu H G, Li Y Y 2011 Chin. Phys. Lett. 28 090507
[35]	Huber M T, Krige J C, Braun H A, Pei X, Neiman A, Moss F 2000 Neurocomputing 32---33 823
[36]	Gu H G, Yang M H, Li L, Liu Z Q, Ren W 2003 Phys. Lett. A 319 89
[37]	Gu H G, Yang M H, Li L, Liu Z Q, Ren W 2003 Int. J. Mod. Phys. B 17 4195
[38]	Mannella R, Palleschi V 1989 Phys. Rev. A 40 3381
[39]	Theiler J, Eubank S, Longtin A, Galdrinkian B 1992 Physica D 58 77
[40]	Sauer T 1994 Phys. Rev. Lett. 72 3811

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