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

白噪声诱发Morris-Lecar模型构成的Ⅱ型兴奋网络产生多次空间相干共振

李玉叶 贾冰 古华光

引用本文:
Citation:

白噪声诱发Morris-Lecar模型构成的Ⅱ型兴奋网络产生多次空间相干共振

李玉叶, 贾冰, 古华光

Multiple spatial coherence resonances induced by white gaussian noise in excitable network composed of Morris-Lecar model with class Ⅱ excitability

Li Yu-Ye, Jia Bing, Gu Hua-Guang
PDF
导出引用
  • 为研究噪声在网络中的作用及对时空行为的影响, 通过电耦合、近邻连接的Morris-Lecar模型构建了同质可兴奋细胞网络. 单元振子的确定性行为表现为Ⅱ型兴奋性的静息. 在高斯白噪声的作用下, 网络会在较大的噪声强度范围产生螺旋波, 以及在某些较小的噪声强度范围产生杂乱的空间结构. 随着噪声强度的增加, 螺旋波的结构会在简单和复杂之间转换, 或与杂乱的空间结构交替出现. 通过空间结构函数及其信噪比的计算, 发现简单螺旋波的信噪比较大, 复杂螺旋波以及杂乱的时空结构的信噪比较小. 信噪比随着噪声强度的增加会出现多次极大值, 说明白噪声可以在可兴奋细胞网络中诱导多次空间相干共振. 研究结果提示现实的可兴奋系统能有多次机会选择不同强度的噪声加以合理利用.
    To study the effect of noise on the network and the influence of noise on the spatio-temporal behaviors of the network, a homogeneous network of excitable cells is constructed, in which the classical Morris-Lecar neuron model behaves as a unit by electric coupling to neighbouring ones. The deterministic behavior of each unit is a resting state corresponding to class Ⅱ excitability. Under the action of white Gaussian noise in the network, spiral wave can be induced within a large range of noise intensity, while disordered spatiotemporal structure is induced within a certain small intensity range. With the increase of noise intensity, spiral wave is characterized by a transition back and forth between simple structure and complex structure, or appears alternately with the disordered structure. By calculating spatial structure function and signal-to-noise ratio (SNR), it is found that the SNR of spiral wave with a simple structure is higher and the SNR becomes lower when the spiral wave has a complex or an even disordered structure. The SNR curve shows that multiple peaks appear with the increase of noise intensity, which indicates that white Gaussian noise can induce the multiple spatial coherence resonance in an excitable cellular network, and suggests that there are many opportunities to select diverse intensity noises to be rationally used in a realistic excitable system.
    • 基金项目: 国家自然科学基金(批准号:11072135, 10772101)和中央高校基本科研业务费基金(批准号:GK200902025)资助的课题.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos 11072135 and 10772101), and the Fundamental Research Funds for the Central Universities (Grant No. GK200902025).
    [1]

    Benzi R, Sutera A, Vulpiani A 1981 J. Phys. A 14 L453

    [2]
    [3]

    Douglass J K, Wilkens L, Pantazelou E, Moss F 1993 Nature 365337

    [4]
    [5]

    Jung P, Mayer-Kress G 1995 Phys. Rev. Lett. 74 2130

    [6]
    [7]

    Hu G, Ditzinger T, Ning C, Haken H 1993 Phys. Rev. Lett. 71 807

    [8]
    [9]

    Zhou C S, Kurths J 2002 Phys. Rev. E 65 040101

    [10]

    Carrillo O, Santos M A, Garca-Ojalvo J, Sancho J 2004 Europhys.Lett. 65 452

    [11]
    [12]

    Perc M 2005 Phys. Rev. E 72 016207

    [13]
    [14]
    [15]

    Yi M, Jia Y, Liu Q, Zhan X 2008 Acta. Phys. Sin. 57 621 (in Chinese)[易鸣, 贾亚, 刘泉, 詹璇 2008 物理学报 57 621]

    [16]

    Higgs M H, Slee S J, Spain W J 2006 J. Neurosci. 26 8787

    [17]
    [18]
    [19]

    Zhang N, Zhang H M, Liu Z Q, Ding X L, Yang M H, Gu H G,Ren W 2009 Chin. Phys. Lett. 26 110501

    [20]
    [21]

    Yuan L, Liu Z Q, Zhang H M, Ding X L, Yang M H, Gu H G, RenW 2011 Chin. Phys. B 20 020508

    [22]

    Perc M 2007 Chaos Soliton. Fract. 31 64

    [23]
    [24]

    Sun X J, Lu Q S 2010 Chin. Phys. B 19 040504

    [25]
    [26]

    Zheng Y H, Lu Q S, Wang Q Y 2009 Int. J. Mod. Phys. C 20 469

    [27]
    [28]

    Sun X J, Perc M, Lu Q S, Kurths J 2010 Chaos 20 033116

    [29]
    [30]

    Wang Q Y, Chen G R, Perc M 2011 PloS ONE 6 e15851

    [31]
    [32]
    [33]

    Ma J, Wang C N, Jin W Y, Wu Y 2010 Appl. Math. Comput. 2173844

    [34]

    Gosak M, Marhl M, Perc M 2009 Physica D 238 506

    [35]
    [36]

    Horikawa Y 2001 Phys. Rev. E 64 031905

    [37]
    [38]

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

    [39]
    [40]
    [41]

    Liu Z Q, Zhang H M, Li Y Y, Hua C C, Gu H G, Ren W 2010Physica A 389 2642

    [42]

    Tateno T, Pakdaman K 2004 Chaos 14 511

    [43]
    [44]

    Tsumoto K, Kitajima H, Yoshinaga T, Aihara K, Kawakami H2006 Neurocomputing 69 293

    [45]
    [46]
    [47]
    [48]

    Izhikevich E M 2000 Int. J. Bifurcat. Chaos 10 1171

    [49]
    [50]

    Hodgkin A 1948 J. Physiol. 107 165

    [51]
    [52]

    Rinzel J, Ermentrout G B 1989 Analysis of neural excitability andoscillations (Cambridge:The MIT Press) p135

    [53]
    [54]

    Tsubo Y, Takada M, Reyes A D, Fukai T 2007 Euro. J. Neurosci.25 3429

    [55]
    [56]
    [57]

    Tateno T, Robinson H 2007 Biophys. J. 92 683

    [58]

    Tateno T, Harsch A, Robinson H 2004 J. Neurophysiol. 92 2283

    [59]
    [60]

    Prescott S A, Ratt S, De Koninck Y, Sejnowski T J 2008 J. Neurophysiol.100 3030

    [61]
    [62]

    Stiefel KM, Gutkin B S, Sejnowski T J 2009 J. Comput. Neurosci.26 289

    [63]
    [64]
    [65]

    Liu Y H, Yang J, Hu S J 2008 J. Comput. Neurosci. 24 95

    [66]
    [67]

    Gutkin B S, Ermentrout G B, Reyes A D 2005 J. Neurophysiol. 941623

    [68]

    Galn R F, Ermentrout G B, Urban N N 2005 Phys. Rev. Lett. 94158101

    [69]
    [70]

    Phoka E, Cuntz H, Roth A, H usser M 2010 PLoS Comput. Biol.6 e1000768

    [71]
    [72]

    Xie Y, Xu J X, Kang Y M, Hu S J, Duan Y B 2004 Chin. Phys.13 1396

    [73]
    [74]

    Bogaard A, Parent J, Zochowski M, Booth V 2009 J. Neurosci. 291677

    [75]
    [76]

    Galn R F, Bard Ermentrout G, Urban N N 2007 Neurocomputing70 2102

    [77]
    [78]
    [79]

    Gu H G, Ren W, Lu Q S, Wu S G, Chen W J 2001 Phys. Lett. A285 63

    [80]

    Gu H G, Zhang H M, Wei C L, Yang M H, Liu Z Q, Ren W 2011Int. J. Mod. Phys. B 25 3977

    [81]
    [82]

    Jia B, Gu H G, Li Y Y 2011 Chin. Phys. Lett. 28 090507

    [83]
    [84]

    Rowat P 2007 Neural Comput. 19 1215

    [85]
    [86]
    [87]

    Fink C G, Booth V, Zochowski M 2011 PLoS Comput. Biol. 7e1002062

    [88]
    [89]

    Vilar J, Rubi J 1997 Phys. Rev. Lett. 78 2882

    [90]
    [91]

    Jiang Y 2005 Phys. Rev. E 71 057103

    [92]

    Liu Z H, Zhou Y R, Zhang A Y, Pang X F 2010 Acta. Phys.Sin.59 699 (in Chinese)[刘志宏, 周玉荣, 张安英, 庞小峰 2010 物理学报 59 699]

    [93]
  • [1]

    Benzi R, Sutera A, Vulpiani A 1981 J. Phys. A 14 L453

    [2]
    [3]

    Douglass J K, Wilkens L, Pantazelou E, Moss F 1993 Nature 365337

    [4]
    [5]

    Jung P, Mayer-Kress G 1995 Phys. Rev. Lett. 74 2130

    [6]
    [7]

    Hu G, Ditzinger T, Ning C, Haken H 1993 Phys. Rev. Lett. 71 807

    [8]
    [9]

    Zhou C S, Kurths J 2002 Phys. Rev. E 65 040101

    [10]

    Carrillo O, Santos M A, Garca-Ojalvo J, Sancho J 2004 Europhys.Lett. 65 452

    [11]
    [12]

    Perc M 2005 Phys. Rev. E 72 016207

    [13]
    [14]
    [15]

    Yi M, Jia Y, Liu Q, Zhan X 2008 Acta. Phys. Sin. 57 621 (in Chinese)[易鸣, 贾亚, 刘泉, 詹璇 2008 物理学报 57 621]

    [16]

    Higgs M H, Slee S J, Spain W J 2006 J. Neurosci. 26 8787

    [17]
    [18]
    [19]

    Zhang N, Zhang H M, Liu Z Q, Ding X L, Yang M H, Gu H G,Ren W 2009 Chin. Phys. Lett. 26 110501

    [20]
    [21]

    Yuan L, Liu Z Q, Zhang H M, Ding X L, Yang M H, Gu H G, RenW 2011 Chin. Phys. B 20 020508

    [22]

    Perc M 2007 Chaos Soliton. Fract. 31 64

    [23]
    [24]

    Sun X J, Lu Q S 2010 Chin. Phys. B 19 040504

    [25]
    [26]

    Zheng Y H, Lu Q S, Wang Q Y 2009 Int. J. Mod. Phys. C 20 469

    [27]
    [28]

    Sun X J, Perc M, Lu Q S, Kurths J 2010 Chaos 20 033116

    [29]
    [30]

    Wang Q Y, Chen G R, Perc M 2011 PloS ONE 6 e15851

    [31]
    [32]
    [33]

    Ma J, Wang C N, Jin W Y, Wu Y 2010 Appl. Math. Comput. 2173844

    [34]

    Gosak M, Marhl M, Perc M 2009 Physica D 238 506

    [35]
    [36]

    Horikawa Y 2001 Phys. Rev. E 64 031905

    [37]
    [38]

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

    [39]
    [40]
    [41]

    Liu Z Q, Zhang H M, Li Y Y, Hua C C, Gu H G, Ren W 2010Physica A 389 2642

    [42]

    Tateno T, Pakdaman K 2004 Chaos 14 511

    [43]
    [44]

    Tsumoto K, Kitajima H, Yoshinaga T, Aihara K, Kawakami H2006 Neurocomputing 69 293

    [45]
    [46]
    [47]
    [48]

    Izhikevich E M 2000 Int. J. Bifurcat. Chaos 10 1171

    [49]
    [50]

    Hodgkin A 1948 J. Physiol. 107 165

    [51]
    [52]

    Rinzel J, Ermentrout G B 1989 Analysis of neural excitability andoscillations (Cambridge:The MIT Press) p135

    [53]
    [54]

    Tsubo Y, Takada M, Reyes A D, Fukai T 2007 Euro. J. Neurosci.25 3429

    [55]
    [56]
    [57]

    Tateno T, Robinson H 2007 Biophys. J. 92 683

    [58]

    Tateno T, Harsch A, Robinson H 2004 J. Neurophysiol. 92 2283

    [59]
    [60]

    Prescott S A, Ratt S, De Koninck Y, Sejnowski T J 2008 J. Neurophysiol.100 3030

    [61]
    [62]

    Stiefel KM, Gutkin B S, Sejnowski T J 2009 J. Comput. Neurosci.26 289

    [63]
    [64]
    [65]

    Liu Y H, Yang J, Hu S J 2008 J. Comput. Neurosci. 24 95

    [66]
    [67]

    Gutkin B S, Ermentrout G B, Reyes A D 2005 J. Neurophysiol. 941623

    [68]

    Galn R F, Ermentrout G B, Urban N N 2005 Phys. Rev. Lett. 94158101

    [69]
    [70]

    Phoka E, Cuntz H, Roth A, H usser M 2010 PLoS Comput. Biol.6 e1000768

    [71]
    [72]

    Xie Y, Xu J X, Kang Y M, Hu S J, Duan Y B 2004 Chin. Phys.13 1396

    [73]
    [74]

    Bogaard A, Parent J, Zochowski M, Booth V 2009 J. Neurosci. 291677

    [75]
    [76]

    Galn R F, Bard Ermentrout G, Urban N N 2007 Neurocomputing70 2102

    [77]
    [78]
    [79]

    Gu H G, Ren W, Lu Q S, Wu S G, Chen W J 2001 Phys. Lett. A285 63

    [80]

    Gu H G, Zhang H M, Wei C L, Yang M H, Liu Z Q, Ren W 2011Int. J. Mod. Phys. B 25 3977

    [81]
    [82]

    Jia B, Gu H G, Li Y Y 2011 Chin. Phys. Lett. 28 090507

    [83]
    [84]

    Rowat P 2007 Neural Comput. 19 1215

    [85]
    [86]
    [87]

    Fink C G, Booth V, Zochowski M 2011 PLoS Comput. Biol. 7e1002062

    [88]
    [89]

    Vilar J, Rubi J 1997 Phys. Rev. Lett. 78 2882

    [90]
    [91]

    Jiang Y 2005 Phys. Rev. E 71 057103

    [92]

    Liu Z H, Zhou Y R, Zhang A Y, Pang X F 2010 Acta. Phys.Sin.59 699 (in Chinese)[刘志宏, 周玉荣, 张安英, 庞小峰 2010 物理学报 59 699]

    [93]
  • [1] 潘军廷, 何银杰, 夏远勋, 张宏. 极化电场对可激发介质中螺旋波的控制. 物理学报, 2020, 69(8): 080503. doi: 10.7498/aps.69.20191934
    [2] 韦宾, 唐国宁, 邓敏艺. 具有早期后除极化现象的可激发系统中螺旋波破碎方式研究. 物理学报, 2018, 67(9): 090501. doi: 10.7498/aps.67.20172505
    [3] 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
    [4] 李伟恒, 潘飞, 黎维新, 唐国宁. 非对称耦合两层可激发介质中的螺旋波动力学. 物理学报, 2015, 64(19): 198201. doi: 10.7498/aps.64.198201
    [5] 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
    [6] 乔成功, 李伟恒, 唐国宁. 细胞外钾离子浓度延迟恢复对螺旋波的影响研究. 物理学报, 2014, 63(23): 238201. doi: 10.7498/aps.63.238201
    [7] 李伟恒, 黎维新, 潘飞, 唐国宁. 两层耦合可激发介质中螺旋波转变为平面波. 物理学报, 2014, 63(20): 208201. doi: 10.7498/aps.63.208201
    [8] 袁国勇, 张焕, 王光瑞. 多可激性障碍下的螺旋波动力学. 物理学报, 2013, 62(16): 160502. doi: 10.7498/aps.62.160502
    [9] 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
    [10] 陈醒基, 乔成功, 王利利, 周振玮, 田涛涛, 唐国宁. 间接延迟耦合可激发介质中螺旋波的演化. 物理学报, 2013, 62(12): 128201. doi: 10.7498/aps.62.128201
    [11] 钱郁. 时空调制对可激发介质螺旋波波头动力学行为影响及控制研究. 物理学报, 2012, 61(15): 158202. doi: 10.7498/aps.61.158202
    [12] 黎广钊, 陈永淇, 唐国宁. 三层弱循环耦合可激发介质中螺旋波动力学. 物理学报, 2012, 61(2): 020502. doi: 10.7498/aps.61.020502
    [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] 周振玮, 陈醒基, 田涛涛, 唐国宁. 耦合可激发介质中螺旋波的控制研究. 物理学报, 2012, 61(21): 210506. doi: 10.7498/aps.61.210506
    [15] 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
    [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] 韦海明, 唐国宁. 离散可激发介质中早期后去极化对螺旋波影响的数值研究. 物理学报, 2011, 60(3): 030501. doi: 10.7498/aps.60.030501
    [18] 戴瑜, 唐国宁. 离散可激发介质激发性降低的几种起因. 物理学报, 2009, 58(3): 1491-1496. doi: 10.7498/aps.58.1491
    [19] 张国勇, 马 军, 甘正宁, 陈 勇. 非均匀可激介质中的螺旋波. 物理学报, 2008, 57(11): 6815-6823. doi: 10.7498/aps.57.6815
    [20] 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
计量
  • 文章访问数:  6849
  • PDF下载量:  776
  • 被引次数: 0
出版历程
  • 收稿日期:  2011-07-04
  • 修回日期:  2012-04-05
  • 刊出日期:  2012-04-05

/

返回文章
返回