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

doi:10.7498/aps.61.070504

摘要

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.

关键词:

Abstract

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.

Keywords:

作者及机构信息

1.
陕西师范大学生命科学学院, 西安 710062

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.

Authors and contacts

1.
College of Life Sciences, Shaanxi Normal University, Xi’an 710062, China

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).

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施引文献

[1]	Benzi R, Sutera A, Vulpiani A 1981 J. Phys. A 14 L453
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[8]
[9]	Zhou C S, Kurths J 2002 Phys. Rev. E 65 040101
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[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 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
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[41]	Liu Z Q, Zhang H M, Li Y Y, Hua C C, Gu H G, Ren W 2010Physica A 389 2642
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[43]
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[78]
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[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]
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[83]
[84]	Rowat P 2007 Neural Comput. 19 1215
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[88]
[89]	Vilar J, Rubi J 1997 Phys. Rev. Lett. 78 2882
[90]
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[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 59 699]
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