梯度耦合下神经元网络中靶波和螺旋波的诱发研究

徐莹; 王春妮; 靳伍银; 马军

doi:10.7498/aps.64.198701

摘要

神经系统内数量众多的神经元电活动的群体行为呈现一定的节律性和自组织性. 当网络局部区域存在异质性或者受到持续周期性刺激, 则在网络内诱发靶波, 且这些靶波如'节拍器'可调制介质中行波的诱发和传播. 基于Hindmarsh-Rose 神经元模型构造了最近邻连接下的二维神经元网络, 研究在非均匀耦合下神经元网络内有序波的诱发问题. 在研究中, 选定网络中心区域的耦合强度最大, 从中心向边界的神经元之间的耦合强度则按照阶梯式下降. 研究结果表明, 在恰当的耦合梯度下, 神经元网络内诱发的靶波或螺旋波可以占据整个网络, 并有效调制神经元网络的群体电活动, 使得整个网络呈现有序性. 特别地, 当初始值为随机值时, 梯度耦合也可以诱发稳定的有序态. 这种梯度耦合对网络群体行为调制的研究结果有助于理解神经元网络的自组织行为.

关键词:

Abstract

Distinct rhythm and self-organization in collective electric activities of neurons could be observed in a neuronal system composed of a large number of neurons. It is found that target wave can be induced in the network by imposing continuous local periodical force or introducing local heterogeneity in the network; and these target waves can regulate the wave propagation and development as pacemaker' in the network or media. A regular neuronal network is constructed in two-dimensional space, in which the local kinetics can be described by Hindmarsh-Rose neuron model, the emergence and development of ordered waves are investigated by introducing gradient coupling between neurons. For simplicity, the center area is selected by the largest coupling intensity, which is gradually decreased at certain step with increasing distance from the center area. It is found that the spiral wave and/or the target wave can be induced by appropriate selection of gradient coupling, and both waves can occupy the network, and then the collective behaviors of the network can be regulated to show ordered states. Particularly, the ordered wave can be effective to dominate the collective behavior of neuronal networks, even as the stochastic values are used for initial states. These results associated with the gradient coupling on the regulating collective behaviors could be useful to understand the self-organization behaviors in neuronal networks.

Keywords:

作者及机构信息

1.
兰州理工大学物理系, 兰州 730050;

2.
兰州理工大学机电学院, 兰州 730050

通信作者: 马军, hyperchaos@163.com

基金项目: 国家自然科学基金(批准号: 11265008, 11365014)资助的课题.

Authors and contacts

1.
Department of Physics, Lanzhou University of Technology, Lanzhou 730050, China;

2.
College of Mechano-Electronic Engineering, University of Technology, Lanzhou 730050, China

Corresponding author: Ma Jun, hyperchaos@163.com

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11265008, 11365014).

参考文献

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[20]	Jia B, Gu H G, Song S L 2013 Sci. China Phys. Mech. 43 518
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[33]	Xie Y, Kang Y M, Liu Y, Wu Y 2014 Sci. China Tech. Sci. 57 914
[34]	Jiao X F, Zhu D F 2014 Sci. China Tech. Sci. 57 923
[35]	Gu H G, Chen S G 2014 Sci. China Tech. Sci. 57 864
[36]	Qin H X, Wu Y, Wang C N, Ma J 2015 Commun. Nonlinear Sci. Numer. Simulat. 23 164
[37]	Sun X J, Shi X 2014 Sci. China Tech. Sci. 57 879
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[41]	Zhang L S, Liao X H, Mi Y Y, Qian Y, Hu G 2014 Chin. Phys. B 23 078906
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[43]	Ma J, Wang C N, Ying H P, Chu R T 2013 Sci. China Phys. Mech. Astro. 56 1126
[44]	Pan J T, Cai M C, Li B W, Zhang H 2013 Phys. Rev. E 87 062907
[45]	Gao X, Zhang H, Zykov V, Bodenschatz E 2014 New J. Phys. 89 022920
[46]	Li B W, Zhang H, Ying H P 2009 Phys. Rev. E 79 026220
[47]	Ma J, Wu Y, Wu N J, Guo H Y 2013 Sci. China Phys. Mech. Astro. 56 952
[48]	Ma J, Liu Q R, Ying H P, Wu Y 2013 Commun. Nonlinear Sci. Numer. Simulat. 18 1665

施引文献

[1]	Shilnikov S 2012 Nonlinear Dyn. SI 68 305
[2]	Rulkov N F 2002 Phys. Rev. E 65 041922
[3]	Storace M, Linaro D, de Lange E 2008 Chaos 18 033128
[4]	Huang X H, Hu G 2014 Chinese Phys. B 23 0108703
[5]	Wang M L, Wang J S 2015 Acta Phys. Sin. 64 108701(in Chinese) [王美丽, 王俊松 2015 64 108701]
[6]	Jiang M, Zhu J, Liu Y P, Yang M P, Tian C P, Jiang S, Wang Y H, Guo H, Wang K Y, Shu Y S 2012 PLoS Biol. 10 e1001324
[7]	Morris C, Lecar H 1981 Biophys. J. 35 193
[8]	Hindmarsh J L, Rose R M 1984 Proc. R. Soc. Lond B Biol. Sci. 221 87
[9]	Ibarz B, Casado J M, Sanjun M A F 2011 Phys. Rep. 501 1
[10]	Zhang LS, Gu W F, Hu G, Mi Y Y 2014 Chinese Phys. B 23 0108902
[11]	Kitajima H, Yoshihara T 2012 Physica D 241 1804
[12]	Jia B 2014 Chin. Phys. B 23 050510
[13]	Storace M, Linaro D, de Lange E 2008 Chaos 18 033128
[14]	Wig G S, Schlaggar B L, Petersen S E 2011 Ann N. Y. Acad. Sci. 1224 126
[15]	Wang H X, Wang Q Y, Zheng Y H 2014 Sci. China Tech. Sci. 57 872
[16]	Torrealdea FJ, Sarasola C, d'Anjou A 2009 Chaos, Solitons Fract. 40 60
[17]	Yu L C, Liu L W 2014 Phys. Rev. E 89 032725
[18]	Wang R B, Zhang Z K, Qu J Y, Cao J T 2011 IEEE T. Neural. Networ. 22 1097
[19]	Ma J, Song X L, Jin W Y, Wang C N 2015 Chaos, Solition. Fract. 80 31
[20]	Jia B, Gu H G, Song S L 2013 Sci. China Phys. Mech. 43 518
[21]	Gu H G, Chen S G 2014 Sci. China Tech. Sci 57 864
[22]	Tang J, Luo J M, Ma J 2013 PLoS One 8 080324
[23]	Yu Y G, Liu F, Wang W 2001 Biol. Cybern. 84 227
[24]	Wang Q Y, Zhang H H, Perc M, Chen G R 2012 Commun. Nonlinear Sci. Numer. Simulat. 17 3979
[25]	Perc M 2008 Phys. Rev. E 78 036105
[26]	Yılmaz E, Uzuntarla M, Ozer M, Perc M 2013 Physica A 392 5735
[27]	Zhang J Q, Wang C D, Wang M S, Huang S F 2011 Nerocomput. 74 2961
[28]	Wang Q Y, Zheng Y H, Ma J 2013 Chaos Solitons Fractals 56 19
[29]	Zeltser L M, Seeley R J, Tschoep M H 2012 Nature Neurosci. 15 1336
[30]	Elbasiouny Sherif M 2014 J. Appl. Physiol. 117 1243
[31]	Yang Z Q, Hao L J 2014 Sci. China Tech. Sci. 57 885
[32]	Wang Q Y, Chen G R, Perc M 2011 PLoS One 6 e15851
[33]	Xie Y, Kang Y M, Liu Y, Wu Y 2014 Sci. China Tech. Sci. 57 914
[34]	Jiao X F, Zhu D F 2014 Sci. China Tech. Sci. 57 923
[35]	Gu H G, Chen S G 2014 Sci. China Tech. Sci. 57 864
[36]	Qin H X, Wu Y, Wang C N, Ma J 2015 Commun. Nonlinear Sci. Numer. Simulat. 23 164
[37]	Sun X J, Shi X 2014 Sci. China Tech. Sci. 57 879
[38]	Baghdadi G, Jafari S, Sprott J C, Towhidkhah F, Hashemi Golpayegani M R 2015 Commun. Nonlinear Sci. Numer. Simulat. 20 174
[39]	Ren G D, Wu G, Ma J, Chen Y 2015 Acta Phys. Sin. 64 058702(in Chinese) [任国栋, 武刚, 马军, 陈旸 2015 64 058702]
[40]	Qin H X, Ma J, Jin W Y, Wang C N 2014 Sci. China Tech. Sci. 57 936
[41]	Zhang L S, Liao X H, Mi Y Y, Qian Y, Hu G 2014 Chin. Phys. B 23 078906
[42]	Li J J, Wu Y, Du M M, Liu W M 2015 Acta Phys. Sin. 64 030503(in Chinese) [李佳佳, 吴莹, 独盟盟, 刘伟明 2015 64 030503]
[43]	Ma J, Wang C N, Ying H P, Chu R T 2013 Sci. China Phys. Mech. Astro. 56 1126
[44]	Pan J T, Cai M C, Li B W, Zhang H 2013 Phys. Rev. E 87 062907
[45]	Gao X, Zhang H, Zykov V, Bodenschatz E 2014 New J. Phys. 89 022920
[46]	Li B W, Zhang H, Ying H P 2009 Phys. Rev. E 79 026220
[47]	Ma J, Wu Y, Wu N J, Guo H Y 2013 Sci. China Phys. Mech. Astro. 56 952
[48]	Ma J, Liu Q R, Ying H P, Wu Y 2013 Commun. Nonlinear Sci. Numer. Simulat. 18 1665

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