Dynamics of a novel chaotic neural firing pattern discovered in experiment and simulated in mathematical model

Gu Hua-Guang; Zhu Zhou; Jia Bing

doi:10.7498/aps.60.100505

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:

Authors and contacts

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

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Cited By

[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 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 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 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 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 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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Vol. 60, Issue 10 - 2011-05-20

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