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

"Hopf/homoclinic"簇放电和"SubHopf/homoclinic"簇放电之间的同步

王付霞 谢勇

引用本文:
Citation:

"Hopf/homoclinic"簇放电和"SubHopf/homoclinic"簇放电之间的同步

王付霞, 谢勇

Synchronization of "Hopf/homoclinic" bursting with "SubHopf/homoclinic" bursting

Wang Fu-Xia, Xie Yong
PDF
导出引用
  • 以修正过的Morris-Lecar神经元模型为例,讨论了"Hopf/homoclinic"簇放电和"SubHopf/homoclinic" 簇放电之间的同步行为.首先,分别考察了同一拓扑类型的两个耦合簇放电神经元的同步行为, 发现"Hopf/homoclinic"簇放电比"SubHopf/homoclinic"簇放电达到膜电位完全同步所需要的耦合强度小, 即前者比后者更容易达到膜电位完全同步.其次,对这两个不同拓扑类型的簇放电神经元的耦合同步行为 进行了讨论.通过数值分析发现随着耦合强度的增加,两种不同类型的簇放电首先达到簇放电同步, 然后当耦合强度足够大时甚至可以达到膜电位完全同步,并且同步后的放电类型更接近容易同步的 簇放电类型,即"Hopf/homoclinic"簇放电.然而令人奇怪的是此时慢变量并没有达到完全同步, 而是相位同步;慢变量之间呈现为一种线性关系.这一点和现有文献的结果截然不同.
    Taking the modified Morris-Lecar neuron model for example, we consider the synchronous behaviour between "Hopf/homoclinic" bursting and "SubHopf/homoclinic" bursting. Firstly, the synchronization between two coupled bursting neurons with the same topological type is investigated numerically, and the results show that the coupling strength reaching the synchronization of the membrane potential of "Hopf/homoclinic" bursting is smaller than that of "SubHopf/homoclinic" bursting, that is to say, the former can reach complete synchrony of the membrane potential more easily than the latter. Secondly, we study the synchronous behavior of two coupled bursting neurons with different topological types by numerical analysis, and find that with the increase of the coupling strength the two different types of bursting neurons reach the bursting-synchrony first, and then they can reach complete synchrony of the membrane potential when the coupling strength is strong enough, and the type of synchronous state is inclined to the type of easy synchronization, namely, "Hopf/homoclinic" bursting. To our surprise, the slow variables exhibit phase synchronization instead of complete synchronization. Moreover, there is a linear relationship between the both slow variables. This point is distinctly different from the results of the existing documents.
    • 基金项目: 国家自然科学基金(批准号: 10972170, 11272241)资助的课题.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 10972170, 11272241).
    [1]

    Lisman J 1997 Trends in Neuroscience 20 38

    [2]

    Wang Q Y, Shi X, Lu Q S 2008 Synchronization dynamics in the coupled system of neurons (1st Ed.) (Beijing: Science Press ) p46 (in Chinese) [王青云, 石霞, 陆启韶 2008 神经元耦合系统的同步动力学(第一版)(北京:科学出版社) 第46页]

    [3]

    Wang W T, Hu S J, H D 2005 Progress in Physiological Sciences 36 137 (in Chinese) [王文挺, 胡三觉, 韩丹 2005 生物力学进展 36 137]

    [4]

    Xu J, Clancy C E 2008 PloS ONE 3 e2056

    [5]

    Xie Y, Xu J X, Kang Y M, Hu S J, Duan Y B 2003 Acta Phys. Sin. 52 1112 (in Chinese) [谢勇, 徐建学, 康艳梅, 胡三觉, 段玉斌 2003 物理学报 52 1112]

    [6]

    Yu H J, Tong W J 2009 Acta Phys. Sin. 58 2977 (in Chinese) [于洪结, 童伟君 2009 物理学报 58 2977]

    [7]

    L L, Li G, Zhang M, Li Y S, Wen L L, Yu M 2011 Acta Phys. Sin. 60 090505 (in Chinese) [吕翎, 李刚, 张檬, 李雨珊, 韦琳玲, 于淼 2011 物理学报 60 090505]

    [8]

    Wu Y, Xu J X, He D H, Jin W Y 2005 Acta Phys. Sin. 54 3457 (in Chinese) [吴瑛, 徐建学, 何岱海, 靳伍银 2005 物理学报 54 3457]

    [9]

    Sleeman B D, Jarvis R J 1985 Ordinary and Partial Differential Equations (Berlin: Springer-Verlag) p304

    [10]

    Teramoto E, Yamaguti M 1987 Mathematical Topics in Population Biology, Morphogenesis and Neurosciences (Berlin: Springer-Verlag) p267

    [11]

    Izhikevich E M 2000 Int. J. Bifurcation and Chaos 10 1171

    [12]

    Izhikevich E M 2007 Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting (London: The MIT Press) p325

    [13]

    Dhamala M, Jirsa V K, Ding M Z 2004 Phys. Rev. Lett. 92 028101

    [14]

    Su J Z, Perez-Gonzalez H, He M 2007 Discrete and Continuous Dynamical Systems, Suppl 946

    [15]

    Yang Z Q, Lu Q S 2007 Sci. China Ser. G: Physics, Mechanics Astronomy 37 440 (in Chinese) [杨卓琴, 陆启韶 2007 中国科学G辑: 物理学、力学、天文学 37 440]

    [16]

    Shi X 2010 Chinese Quarterly of Mechanics 1 52 (in Chinese) [石霞 2010 力学季刊 1 52]

    [17]

    Wu Y, Xu J X, Jin W Y 2005 Lecture Notes in Computer Science 3496 302

    [18]

    Wu Y, Xu J X, He M 2005 Lecture Notes in Computer Science 3610 508

    [19]

    Shen Y, Hou Z H, Xin H W 2008 Phys. Rev. E 77 031920

    [20]

    Wang H X, Lu Q S, Wang Q Y 2008 Communications in Nonlinear Science and Numerical Simulation 13 1668

    [21]

    Izhikevich E M 2001 SIAM Review 43 315

    [22]

    Gu H G, Li L, Yang M H, Liu Z Q, Ren W 2003 Acta Biophysica Sinica 19 69 (in Chinese) [古华光, 李莉, 杨明浩, 刘志强, 任维 2003 生物物理学报 19 69]

    [23]

    Wang H X, Lu Q S, Shi X 2010 Chin. Phys. B 19 06059

  • [1]

    Lisman J 1997 Trends in Neuroscience 20 38

    [2]

    Wang Q Y, Shi X, Lu Q S 2008 Synchronization dynamics in the coupled system of neurons (1st Ed.) (Beijing: Science Press ) p46 (in Chinese) [王青云, 石霞, 陆启韶 2008 神经元耦合系统的同步动力学(第一版)(北京:科学出版社) 第46页]

    [3]

    Wang W T, Hu S J, H D 2005 Progress in Physiological Sciences 36 137 (in Chinese) [王文挺, 胡三觉, 韩丹 2005 生物力学进展 36 137]

    [4]

    Xu J, Clancy C E 2008 PloS ONE 3 e2056

    [5]

    Xie Y, Xu J X, Kang Y M, Hu S J, Duan Y B 2003 Acta Phys. Sin. 52 1112 (in Chinese) [谢勇, 徐建学, 康艳梅, 胡三觉, 段玉斌 2003 物理学报 52 1112]

    [6]

    Yu H J, Tong W J 2009 Acta Phys. Sin. 58 2977 (in Chinese) [于洪结, 童伟君 2009 物理学报 58 2977]

    [7]

    L L, Li G, Zhang M, Li Y S, Wen L L, Yu M 2011 Acta Phys. Sin. 60 090505 (in Chinese) [吕翎, 李刚, 张檬, 李雨珊, 韦琳玲, 于淼 2011 物理学报 60 090505]

    [8]

    Wu Y, Xu J X, He D H, Jin W Y 2005 Acta Phys. Sin. 54 3457 (in Chinese) [吴瑛, 徐建学, 何岱海, 靳伍银 2005 物理学报 54 3457]

    [9]

    Sleeman B D, Jarvis R J 1985 Ordinary and Partial Differential Equations (Berlin: Springer-Verlag) p304

    [10]

    Teramoto E, Yamaguti M 1987 Mathematical Topics in Population Biology, Morphogenesis and Neurosciences (Berlin: Springer-Verlag) p267

    [11]

    Izhikevich E M 2000 Int. J. Bifurcation and Chaos 10 1171

    [12]

    Izhikevich E M 2007 Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting (London: The MIT Press) p325

    [13]

    Dhamala M, Jirsa V K, Ding M Z 2004 Phys. Rev. Lett. 92 028101

    [14]

    Su J Z, Perez-Gonzalez H, He M 2007 Discrete and Continuous Dynamical Systems, Suppl 946

    [15]

    Yang Z Q, Lu Q S 2007 Sci. China Ser. G: Physics, Mechanics Astronomy 37 440 (in Chinese) [杨卓琴, 陆启韶 2007 中国科学G辑: 物理学、力学、天文学 37 440]

    [16]

    Shi X 2010 Chinese Quarterly of Mechanics 1 52 (in Chinese) [石霞 2010 力学季刊 1 52]

    [17]

    Wu Y, Xu J X, Jin W Y 2005 Lecture Notes in Computer Science 3496 302

    [18]

    Wu Y, Xu J X, He M 2005 Lecture Notes in Computer Science 3610 508

    [19]

    Shen Y, Hou Z H, Xin H W 2008 Phys. Rev. E 77 031920

    [20]

    Wang H X, Lu Q S, Wang Q Y 2008 Communications in Nonlinear Science and Numerical Simulation 13 1668

    [21]

    Izhikevich E M 2001 SIAM Review 43 315

    [22]

    Gu H G, Li L, Yang M H, Liu Z Q, Ren W 2003 Acta Biophysica Sinica 19 69 (in Chinese) [古华光, 李莉, 杨明浩, 刘志强, 任维 2003 生物物理学报 19 69]

    [23]

    Wang H X, Lu Q S, Shi X 2010 Chin. Phys. B 19 06059

  • [1] 梁艳美, 陆博, 古华光. 利用双慢变量的快慢变量分离分析新脑皮层神经元Wilson模型的复杂电活动. 物理学报, 2022, 71(23): 230502. doi: 10.7498/aps.71.20221416
    [2] 白婧, 关富荣, 唐国宁. 神经元网络中局部同步引发的各种效应. 物理学报, 2021, 70(17): 170502. doi: 10.7498/aps.70.20210142
    [3] 谢盈, 朱志刚, 张晓锋, 任国栋. 光电流驱动下非线性神经元电路的放电模式控制. 物理学报, 2021, 70(21): 210502. doi: 10.7498/aps.70.20210676
    [4] 丁学利, 古华光, 贾冰, 李玉叶. 抑制性自突触诱发耦合Morris-Lecar神经元电活动的超前同步. 物理学报, 2021, 70(21): 218701. doi: 10.7498/aps.70.20210912
    [5] 赵雅琪, 刘谋天, 赵勇, 段利霞. 耦合前包钦格复合体神经元中复杂混合簇放电的动力学. 物理学报, 2021, 70(12): 120501. doi: 10.7498/aps.70.20210093
    [6] 张秀芳, 马军, 徐莹, 任国栋. 光电管耦合FitzHugh-Nagumo神经元的同步. 物理学报, 2021, 70(9): 090502. doi: 10.7498/aps.70.20201953
    [7] 姜伊澜, 陆博, 张万芹, 古华光. 快自突触反馈诱发混合簇放电的反常变化及分岔机制. 物理学报, 2021, 70(17): 170501. doi: 10.7498/aps.70.20210208
    [8] 华洪涛, 陆博, 古华光. 兴奋性自突触引起神经簇放电频率降低或增加的非线性机制. 物理学报, 2020, 69(9): 090502. doi: 10.7498/aps.69.20191709
    [9] 郑志刚, 翟云, 王学彬, 陈宏斌, 徐灿. 耦合相振子系统同步的序参量理论. 物理学报, 2020, 69(8): 080502. doi: 10.7498/aps.69.20191968
    [10] 杨永霞, 李玉叶, 古华光. Pre-Bötzinger复合体的从簇到峰放电的同步转迁及分岔机制. 物理学报, 2020, 69(4): 040501. doi: 10.7498/aps.69.20191509
    [11] 曹奔, 关利南, 古华光. 兴奋性作用诱发神经簇放电个数不增反降的分岔机制. 物理学报, 2018, 67(24): 240502. doi: 10.7498/aps.67.20181675
    [12] 谢勇, 程建慧. 计算相位响应曲线的方波扰动直接算法. 物理学报, 2017, 66(9): 090501. doi: 10.7498/aps.66.090501
    [13] 任国栋, 武刚, 马军, 陈旸. 一类自突触作用下神经元电路的设计和模拟. 物理学报, 2015, 64(5): 058702. doi: 10.7498/aps.64.058702
    [14] 李佳佳, 吴莹, 独盟盟, 刘伟明. 电磁辐射诱发神经元放电节律转迁的动力学行为研究. 物理学报, 2015, 64(3): 030503. doi: 10.7498/aps.64.030503
    [15] 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
    [16] 王兴元, 任小丽, 张永雷. 参数未知神经元模型的全阶与降阶最优同步. 物理学报, 2012, 61(6): 060508. doi: 10.7498/aps.61.060508
    [17] 杨卓琴, 管亭亭, 甘春标, 张矫瑛. 双参数分岔平面内胰腺细胞的簇放电分析. 物理学报, 2011, 60(11): 110202. doi: 10.7498/aps.60.110202
    [18] 何国光, 朱萍, 陈宏平, 谢小平. 阈值耦合混沌神经元的同步研究. 物理学报, 2010, 59(8): 5307-5312. doi: 10.7498/aps.59.5307
    [19] 刘勇, 谢勇. 分数阶FitzHugh-Nagumo模型神经元的动力学特性及其同步. 物理学报, 2010, 59(3): 2147-2155. doi: 10.7498/aps.59.2147
    [20] 吴 王莹, 徐健学, 何岱海, 靳伍银. 两个非耦合Hindmarsh-Rose神经元同步的非线性特征研究. 物理学报, 2005, 54(7): 3457-3464. doi: 10.7498/aps.54.3457
计量
  • 文章访问数:  5290
  • PDF下载量:  512
  • 被引次数: 0
出版历程
  • 收稿日期:  2012-06-18
  • 修回日期:  2012-07-30
  • 刊出日期:  2013-01-05

/

返回文章
返回