搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

Hindmarsh-Rose神经元阵列自发产生螺旋波的研究

汪芃 李倩昀 唐国宁

引用本文:
Citation:

Hindmarsh-Rose神经元阵列自发产生螺旋波的研究

汪芃, 李倩昀, 唐国宁

Spontaneous generation of spiral wave in the array of Hindmarsh-Rose neurons

Wang Peng, Li Qian-Yun, Tang Guo-Ning
PDF
导出引用
  • 采用Hindmarsh-Rose(HR)神经元模型,研究了二维神经元阵列系统从一个具有随机相位分布的初态演化最终是否能自发产生螺旋波的问题.数值结果表明:系统是否出现螺旋波与单个HR神经元的状态、系统的初态和耦合强度有关,其中单个HR神经元的振荡状态起主要作用.当单个HR神经元处于一周期振荡态时,在一定的耦合强度范围内系统都会自发出现多个螺旋波和螺旋波对,出现螺旋波与系统初态无关,只要适当选择耦合强度,在系统中可以出现单个螺旋波.当耦合强度超过某一阈值后,继续增加耦合强度,系统会呈现三种不同的动力学行为,分别与三类初态有关.系统从第一类初态演化将偶尔出现单个螺旋波,系统从第二类和第三类初态演化将分别出现间歇性全局同步振荡和振荡死亡.当单个神经元处于二周期态时,只有当系统神经元的初相位比较均匀分布时,系统才能自发出现螺旋波,而且出现螺旋波的耦合强度范围大为减少.当神经元处于更高的周期态时,系统一般不容易自发出现螺旋波.这些结果有助于人们了解大脑皮层自发产生螺旋波的机制.
    Spiral waves have been reported to be existent in the neocortex, during pharmacologically induced oscillations and sleep-like states. In the last decades, theoretical studies have demonstrated an underlying mechanism of the generation of spiral waves in a heart system. Nevertheless, how can a neural system produce spontaneous spiral wave and whether this behavior is sensitive to the dynamics of isolated neurons have not been systematically studied yet. In this paper we propose a modified Hindmarsh-Rose (HR) neuron model to study whether spiral wave can occur spontaneously in a two-dimensional array of HR neurons, which evolves from the initial state with a random phase distribution. The simulation results show that whether spiral wave can occur spontaneously in the system depends on the state of the single HR neuron, initial state of system and coupling strength. Especially, the state of the single HR neuron plays a central role. When the single HR neuron is in the state of period 1 spike, multiple spiral waves and spiral pairs can be generated spontaneously in the system for a certain range of coupling strength. In this case, the formations of spiral waves are completely independent of the initial state of the system, and as long as choosing an appropriate coupling strength, a single spiral wave can be found in the system. Furthermore, when the coupling strength exceeds a certain threshold value, the system will exhibit three kinds of dynamical behaviors, and correspond to three kinds of the different initial states, respectively. When system evolves from the first kind of initial state, the single spiral wave can be found occasionally in the system. When the system evolves from the second or third kind of initial state, the oscillation with intermittently global synchronization and oscillation death can be observed in the system, respectively. When a single HR neuron is in the state of period 2 spike, the spiral wave can appear spontaneously in the system only when the phase distribution of the initial state approaches to a uniform distribution. Moreover, the range of coupling strength on the generation of spiral wave is smaller than that of period 1 spike. When the single HR neuron is in a higher periodic state, it is difficult to generate spontaneously spiral wave in the system. These results are useful in understanding the spontaneous generation of spiral waves in the neocortex.
      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]

    Winfree A T 1972 Science 175 634

    [2]

    Larionova Y, Egorov O, Cabrera-Granado E, Esteban-Martin A 2005 Phys. Rev. A 72 033825

    [3]

    Plapp B P, Egolf D A, Bodenschatz E, Pesch W 1998 Phys. Rev. Lett. 81 5334

    [4]

    Mller S C, Plesser T, Hess B 1985 Science 230 661

    [5]

    Vanag V K, Epstein I R 2001 Science 294 835

    [6]

    Foerster P, Mller S C, Hess B 1990 Development 109 11

    [7]

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

    [8]

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

    [9]

    Huang X, Troy W C, Yang Q, Ma H, Laing C R, Schiff S T, Wu J Y 2004 J. Neurosci. 24 9897

    [10]

    Chen J X, Zhang H, Qiao L Y, Liang H, Sun W G 2018 Commun. Nonlinear Sci. Numer. Simulat. 54 202

    [11]

    Chen J X, Guo M M, Ma J 2016 Europhys. Lett. 113 38004

    [12]

    Chen J X, Liang P, Zheng Q, Zhao Y H, Ying H P 2014 Chaos 24 033103

    [13]

    Pumir A, Nikolski V, Horning M, Isomura A, Agladze K, Yoshikawa K, Gilmour R, Bodenschatz E, Krinsky V 2007 Phys. Rev. Lett. 99 208101

    [14]

    Gan Z N, Cheng X M 2010 Chin. Phys. B 19 050514

    [15]

    Viventi J, Kim D H, Vigeland L, Frechette E S, Blanco J A, Kim Y S 2011 Nat Neurosci. 14 1599

    [16]

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

    [17]

    Garca-Ojalvo J, Schimansky-Geier L 1999 Europhys. Lett. 47 298

    [18]

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

    [19]

    Li Y Y, Zhang H M, Wei C L, Yang M H, Gu H G, Ren W 2009 Chin. Phys. Lett. 26 030504

    [20]

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

    [21]

    Jung P, Cornell-Bell A, Moss F, Kadar S, Wang J, Showalter K 1998 Chaos 8 567

    [22]

    Ullner E, Zaikin A, Garca-Ojalvo J, Kurths J 2003 Phys. Rev. Lett. 91 180601

    [23]

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

    [24]

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

    [25]

    Jiruska P, De-Curtis M, Jefferys J G R, Schevon C A, Schiff S J, Schindler K 2013 J. Physiol. 591 787

  • [1]

    Winfree A T 1972 Science 175 634

    [2]

    Larionova Y, Egorov O, Cabrera-Granado E, Esteban-Martin A 2005 Phys. Rev. A 72 033825

    [3]

    Plapp B P, Egolf D A, Bodenschatz E, Pesch W 1998 Phys. Rev. Lett. 81 5334

    [4]

    Mller S C, Plesser T, Hess B 1985 Science 230 661

    [5]

    Vanag V K, Epstein I R 2001 Science 294 835

    [6]

    Foerster P, Mller S C, Hess B 1990 Development 109 11

    [7]

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

    [8]

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

    [9]

    Huang X, Troy W C, Yang Q, Ma H, Laing C R, Schiff S T, Wu J Y 2004 J. Neurosci. 24 9897

    [10]

    Chen J X, Zhang H, Qiao L Y, Liang H, Sun W G 2018 Commun. Nonlinear Sci. Numer. Simulat. 54 202

    [11]

    Chen J X, Guo M M, Ma J 2016 Europhys. Lett. 113 38004

    [12]

    Chen J X, Liang P, Zheng Q, Zhao Y H, Ying H P 2014 Chaos 24 033103

    [13]

    Pumir A, Nikolski V, Horning M, Isomura A, Agladze K, Yoshikawa K, Gilmour R, Bodenschatz E, Krinsky V 2007 Phys. Rev. Lett. 99 208101

    [14]

    Gan Z N, Cheng X M 2010 Chin. Phys. B 19 050514

    [15]

    Viventi J, Kim D H, Vigeland L, Frechette E S, Blanco J A, Kim Y S 2011 Nat Neurosci. 14 1599

    [16]

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

    [17]

    Garca-Ojalvo J, Schimansky-Geier L 1999 Europhys. Lett. 47 298

    [18]

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

    [19]

    Li Y Y, Zhang H M, Wei C L, Yang M H, Gu H G, Ren W 2009 Chin. Phys. Lett. 26 030504

    [20]

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

    [21]

    Jung P, Cornell-Bell A, Moss F, Kadar S, Wang J, Showalter K 1998 Chaos 8 567

    [22]

    Ullner E, Zaikin A, Garca-Ojalvo J, Kurths J 2003 Phys. Rev. Lett. 91 180601

    [23]

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

    [24]

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

    [25]

    Jiruska P, De-Curtis M, Jefferys J G R, Schevon C A, Schiff S J, Schindler K 2013 J. Physiol. 591 787

  • [1] 黄志精, 李倩昀, 白婧, 唐国宁. 在具有排斥耦合的神经元网络中有序斑图的熵测量. 物理学报, 2019, 68(11): 110503. doi: 10.7498/aps.68.20190231
    [2] 汪芃, 李倩昀, 黄志精, 唐国宁. 在兴奋-抑制混沌神经元网络中有序波的自发形成. 物理学报, 2018, 67(17): 170501. doi: 10.7498/aps.67.20180506
    [3] 乔晓粉, 李晓莉, 刘赫男, 石薇, 刘雪璐, 吴江滨, 谭平恒. 悬浮二维晶体材料反射光谱和光致发光光谱的周期性振荡现象. 物理学报, 2016, 65(13): 136801. doi: 10.7498/aps.65.136801
    [4] 徐莹, 王春妮, 靳伍银, 马军. 梯度耦合下神经元网络中靶波和螺旋波的诱发研究. 物理学报, 2015, 64(19): 198701. doi: 10.7498/aps.64.198701
    [5] 曾果, 李兴源, 刘天琪, 赵睿. 同时抑制低频振荡和次同步振荡的多通道广域自适应阻尼控制. 物理学报, 2014, 63(22): 228801. doi: 10.7498/aps.63.228801
    [6] 陈石, 王辉, 沈胜强, 梁刚涛. 液滴振荡模型及与数值模拟的对比. 物理学报, 2013, 62(20): 204702. doi: 10.7498/aps.62.204702
    [7] 赵龙, 杨继平, 郑艳红. 神经元网络螺旋波诱发机理研究. 物理学报, 2013, 62(2): 028701. doi: 10.7498/aps.62.028701
    [8] 邝玉兰, 唐国宁. 利用短期心脏记忆消除螺旋波和时空混沌. 物理学报, 2012, 61(19): 190501. doi: 10.7498/aps.61.190501
    [9] 董丽芳, 白占国, 贺亚峰. 非均匀可激发介质中的稀密螺旋波. 物理学报, 2012, 61(12): 120509. doi: 10.7498/aps.61.120509
    [10] 邝玉兰, 唐国宁. 心脏中的螺旋波和时空混沌的抑制研究. 物理学报, 2012, 61(10): 100504. doi: 10.7498/aps.61.100504
    [11] 刘少宝, 吴莹, 郝忠文, 李银军, 贾宁. 钠离子和钾离子通道噪声扰动对神经网络时空模式的影响. 物理学报, 2012, 61(2): 020503. doi: 10.7498/aps.61.020503
    [12] 吴望生, 唐国宁. 不同耦合下混沌神经元网络的同步. 物理学报, 2012, 61(7): 070505. doi: 10.7498/aps.61.070505
    [13] 马军, 谢振博, 陈江星. 热敏神经元网络中螺旋波死亡和破裂的数值模拟. 物理学报, 2012, 61(3): 038701. doi: 10.7498/aps.61.038701
    [14] 韦海明, 唐国宁. 交替行为对螺旋波影响的数值模拟研究. 物理学报, 2011, 60(4): 040504. doi: 10.7498/aps.60.040504
    [15] 王金平, 许建平, 徐杨军. 恒定导通时间控制buck变换器多开关周期振荡现象分析. 物理学报, 2011, 60(5): 058401. doi: 10.7498/aps.60.058401
    [16] 田昌海, 邓敏艺, 孔令江, 刘慕仁. 螺旋波动力学性质的元胞自动机有向小世界网络研究. 物理学报, 2011, 60(8): 080505. doi: 10.7498/aps.60.080505
    [17] 杨先清, 刘甫, 贾燕, 邓敏, 郭海萍, 唐刚. 垂直振动颗粒混合气体的振荡现象研究. 物理学报, 2010, 59(2): 1116-1122. doi: 10.7498/aps.59.1116
    [18] 甘正宁, 马 军, 张国勇, 陈 勇. 小世界网络上螺旋波失稳的研究. 物理学报, 2008, 57(9): 5400-5406. doi: 10.7498/aps.57.5400
    [19] 谢 芳, 朱亚波, 张兆慧, 张 林. 碳纳米管振荡的分子动力学模拟. 物理学报, 2008, 57(9): 5833-5837. doi: 10.7498/aps.57.5833
    [20] 马 军, 靳伍银, 李延龙, 陈 勇. 随机相位扰动抑制激发介质中漂移的螺旋波. 物理学报, 2007, 56(4): 2456-2465. doi: 10.7498/aps.56.2456
计量
  • 文章访问数:  6294
  • PDF下载量:  163
  • 被引次数: 0
出版历程
  • 收稿日期:  2017-09-27
  • 修回日期:  2017-10-30
  • 刊出日期:  2018-02-05

/

返回文章
返回