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在兴奋-抑制混沌神经元网络中有序波的自发形成

汪芃 李倩昀 黄志精 唐国宁

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在兴奋-抑制混沌神经元网络中有序波的自发形成

汪芃, 李倩昀, 黄志精, 唐国宁

Spontaneous formation of ordered waves in chaotic neuronal network with excitory-inhibitory connections

Wang Peng, Li Qian-Yun, Huang Zhi-Jing, Tang Guo-Ning
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  • 大脑皮层在一定条件下可以自发出现螺旋波和平面波,为了了解这些有序波的产生机制,构造了一个双层的二维神经元网络.该网络由最近邻兴奋性耦合和长程抑制性耦合层组成,采用修改后的Hindmarsh-Rose神经元模型研究了该混沌神经元网络从具有随机相位分布的初态演化是否能自发出现各种有序波.数值模拟结果表明:当抑制性耦合强度比较小时,系统一般不会自发出现有序波;在兴奋性耦合强度足够大的情况下,抑制性耦合强度越大,系统越容易产生有序波.系统出现不同的有序波与系统初态和耦合强度有密切关系,适当选择兴奋性和抑制性耦合的耦合强度,系统会自发出现迷宫斑图、平面波、单螺旋波、多螺旋波、旋转方向相反的螺旋波对、双臂螺旋波、靶波、向内方形波等有序波斑图.螺旋波、迷宫斑图和内向方形波出现概率分别达到27.5%,21.5%和10.0%,这里的迷宫斑图是由不同传播方向的许多平面波组成,其他有序波出现概率比较小.研究结果有助于理解发生在大脑皮层中的自组织现象.
    Spiral waves are a particular form of propagating waves, which rotate around a center point known as a rotor. Spiral waves have been found to play an important role in cardiac arrhythmia. Using voltage-sensitive dye imaging, one can find that spiral waves and plannar waves can occur in the mammalian cortex in vivo. The electrode array conduces to discovering that the seizures may manifest as recurrent spiral waves which propagate in the neocortex. However, the formation mechanism of the ordered waves and its potential function in the nervous system remain uncertain. In order to understand the formation mechanism of the ordered waves, we construct a double-layer two-dimensional -network of neuron, which is composed of nearest-neighbor excitatory coupling and long-range inhibitory coupling layers. The inhibitory grid points account for 25% of total number of grid points in the network. We propose a modified Hindmarsh-Rose neuron model to study whether differently ordered waves can occur spontaneously in the chaotic neuronal network evolving from the initial state with a random phase distribution. The numerical simulation results show that when the inhibitory coupling strength is small the spontaneous formation of ordered wave does not generally appear in the network. The larger inhibitory coupling strength, the more easily the system generates an ordered wave for sufficiently large strength of excitatory coupling. The appearance of differently ordered waves is closely related to the initial state of the system and coupling strength. As the excitatory and inhibitory coupling strengths are appropriately selected, the system can spontaneously generate the maze pattern, planar wave, single spiral wave, multiple spiral wave, paired spiral waves rotating in the opposite directions, two-arm spiral wave, target wave and inward square wave and so on. The probability for spontaneously forming a single spiral wave is far less than that for forming a small spiral wave. The occurrence probabilities of spiral wave, maze pattern and inward square wave reach 27.5%, 21.5% and 10%, respectively. The maze pattern is composed of many plane waves with different propagation directions. The occurrence probabilities of other ordered waves are quite small. These results conduce to understanding the self-organization phenomena occurring in the cerebral cortex.
      通信作者: 唐国宁, tangguoning@sohu.com
    • 基金项目: 国家自然科学基金(批准号:11565005,11365003,11747307)资助的课题.
      Corresponding author: Tang Guo-Ning, tangguoning@sohu.com
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11565005, 11365003, 11747307).
    [1]

    Sato T K, Nauhaus I, Carandini M 2012 Neuron 75 218

    [2]

    Huang X Y, Xu W F, Liang J M, Takagaki K, Gao X, Wu J Y 2010 Neuron 68 978

    [3]

    Huang X Y, William C T, Yang Q, Ma H T, Carlo R L, Steven J S, Wu J Y 2004 J. Neurosci. 24 9897

    [4]

    Viventi J, Kim D H, Vigeland L, Frechette E S, Blanco J A, Kim Y S, Avrin A E, Tiruvadi V R, Hwang S W, Vanleer A C, Wulsin D F, Davis K, Gelber C E, Palmer L, Spiegel J V, Wu J, Xiao J L, Huang Y G, Contreras D, Rogers J A, Litt B 2011 Nat. Neurosci. 14 1599

    [5]

    Davidenko J M, Pertsov A V, Salomonsz, Baxter W, Jalife J 1992 Nature 355 349

    [6]

    Yu Y F, Santos L M, Mattiace L A, Costa M L, Ferreira L C, Benabou K, Kim A H, Abrahams J, Bennett M V L, Rozental R 2012 PNAS 109 2585

    [7]

    Wang Q Y, Perc M, Duan Z S, Chen G R 2008 Phys. Lett. A 372 5681

    [8]

    Ma J, Huang L, Ying H P, Pu Z S 2012 Chin. Sci. Bull. 57 2094

    [9]

    Gu H G, Jia B, Li Y Y, Chen G R 2013 Physica A 392 1361

    [10]

    Hu B, Ma J, Tang J 2013 PloS One 8 e0069251

    [11]

    Qin H X, Ma J, Wang C N, Chu R T 2014 Sci. China:Phys. Mech. Astron. 57 1918

    [12]

    Ma J, Tang J 2015 Sci. China:Tech. Sci. 58 2038

    [13]

    Yao Y G, Deng H Y, Ma C Z, Yi M, Ma J 2017 PloS One 12 e0171273

    [14]

    Yao Y G, Deng H Y, Ma C Z, Yi M, Ma J 2017 Scientific Reports 7 43151

    [15]

    Jung P, Cornell-Bell A, Madden K S, Moss F 1998 J. Neurophysiol. 79 1098

    [16]

    Ma J, Wu Y, Ying H P, Jia Y 2011 Chin. Sci. Bull. 56 151

    [17]

    Wang C N, Ma J, Hu B L, Jin W Y 2015 Int. J. Mod. Phys. B 29 1550043

    [18]

    Wang P, Li Q Y, Tang G N 2018 Acta Phys. Sin. 67 030502 (in Chinese)[汪芃, 李倩昀, 唐国宁 2018 物理学报 67 030502]

    [19]

    Fohlmeister C, Gerstner W, Ritz R, Hemmen J L 1995 Neural Comput. 7 905

    [20]

    Xiao W W, Gu H G, Liu M R 2016 Sci. China:Tech. Sci. 59 1943

    [21]

    Tao Y, Gu H G 2017 Int. J. Mod. Phys. B 31 1750179

    [22]

    Okun M, Lampl I 2008 Nat. Neurosci. 11 535

    [23]

    Soriano J, Martínez M R, Tlusty T, Moses E 2008 PNAS 105 13758

    [24]

    Hindmarsh J L, Rose R M 1984 Proc. R. Soc. Lond. B 221 87

    [25]

    Adhikari B M, Prasad A, Dhamala M 2011 Chaos 21 023116

  • [1]

    Sato T K, Nauhaus I, Carandini M 2012 Neuron 75 218

    [2]

    Huang X Y, Xu W F, Liang J M, Takagaki K, Gao X, Wu J Y 2010 Neuron 68 978

    [3]

    Huang X Y, William C T, Yang Q, Ma H T, Carlo R L, Steven J S, Wu J Y 2004 J. Neurosci. 24 9897

    [4]

    Viventi J, Kim D H, Vigeland L, Frechette E S, Blanco J A, Kim Y S, Avrin A E, Tiruvadi V R, Hwang S W, Vanleer A C, Wulsin D F, Davis K, Gelber C E, Palmer L, Spiegel J V, Wu J, Xiao J L, Huang Y G, Contreras D, Rogers J A, Litt B 2011 Nat. Neurosci. 14 1599

    [5]

    Davidenko J M, Pertsov A V, Salomonsz, Baxter W, Jalife J 1992 Nature 355 349

    [6]

    Yu Y F, Santos L M, Mattiace L A, Costa M L, Ferreira L C, Benabou K, Kim A H, Abrahams J, Bennett M V L, Rozental R 2012 PNAS 109 2585

    [7]

    Wang Q Y, Perc M, Duan Z S, Chen G R 2008 Phys. Lett. A 372 5681

    [8]

    Ma J, Huang L, Ying H P, Pu Z S 2012 Chin. Sci. Bull. 57 2094

    [9]

    Gu H G, Jia B, Li Y Y, Chen G R 2013 Physica A 392 1361

    [10]

    Hu B, Ma J, Tang J 2013 PloS One 8 e0069251

    [11]

    Qin H X, Ma J, Wang C N, Chu R T 2014 Sci. China:Phys. Mech. Astron. 57 1918

    [12]

    Ma J, Tang J 2015 Sci. China:Tech. Sci. 58 2038

    [13]

    Yao Y G, Deng H Y, Ma C Z, Yi M, Ma J 2017 PloS One 12 e0171273

    [14]

    Yao Y G, Deng H Y, Ma C Z, Yi M, Ma J 2017 Scientific Reports 7 43151

    [15]

    Jung P, Cornell-Bell A, Madden K S, Moss F 1998 J. Neurophysiol. 79 1098

    [16]

    Ma J, Wu Y, Ying H P, Jia Y 2011 Chin. Sci. Bull. 56 151

    [17]

    Wang C N, Ma J, Hu B L, Jin W Y 2015 Int. J. Mod. Phys. B 29 1550043

    [18]

    Wang P, Li Q Y, Tang G N 2018 Acta Phys. Sin. 67 030502 (in Chinese)[汪芃, 李倩昀, 唐国宁 2018 物理学报 67 030502]

    [19]

    Fohlmeister C, Gerstner W, Ritz R, Hemmen J L 1995 Neural Comput. 7 905

    [20]

    Xiao W W, Gu H G, Liu M R 2016 Sci. China:Tech. Sci. 59 1943

    [21]

    Tao Y, Gu H G 2017 Int. J. Mod. Phys. B 31 1750179

    [22]

    Okun M, Lampl I 2008 Nat. Neurosci. 11 535

    [23]

    Soriano J, Martínez M R, Tlusty T, Moses E 2008 PNAS 105 13758

    [24]

    Hindmarsh J L, Rose R M 1984 Proc. R. Soc. Lond. B 221 87

    [25]

    Adhikari B M, Prasad A, Dhamala M 2011 Chaos 21 023116

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出版历程
  • 收稿日期:  2018-03-21
  • 修回日期:  2018-05-22
  • 刊出日期:  2018-09-05

在兴奋-抑制混沌神经元网络中有序波的自发形成

  • 1. 广西师范大学物理科学与技术学院, 桂林 541004
  • 通信作者: 唐国宁, tangguoning@sohu.com
    基金项目: 国家自然科学基金(批准号:11565005,11365003,11747307)资助的课题.

摘要: 大脑皮层在一定条件下可以自发出现螺旋波和平面波,为了了解这些有序波的产生机制,构造了一个双层的二维神经元网络.该网络由最近邻兴奋性耦合和长程抑制性耦合层组成,采用修改后的Hindmarsh-Rose神经元模型研究了该混沌神经元网络从具有随机相位分布的初态演化是否能自发出现各种有序波.数值模拟结果表明:当抑制性耦合强度比较小时,系统一般不会自发出现有序波;在兴奋性耦合强度足够大的情况下,抑制性耦合强度越大,系统越容易产生有序波.系统出现不同的有序波与系统初态和耦合强度有密切关系,适当选择兴奋性和抑制性耦合的耦合强度,系统会自发出现迷宫斑图、平面波、单螺旋波、多螺旋波、旋转方向相反的螺旋波对、双臂螺旋波、靶波、向内方形波等有序波斑图.螺旋波、迷宫斑图和内向方形波出现概率分别达到27.5%,21.5%和10.0%,这里的迷宫斑图是由不同传播方向的许多平面波组成,其他有序波出现概率比较小.研究结果有助于理解发生在大脑皮层中的自组织现象.

English Abstract

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