双色噪声激励下FHN神经元系统的稳态性质

杨亚强; 王参军

doi:10.7498/aps.61.120507

摘要

应用统一色噪声理论研究了双色噪声激励下一维FitzHugh-Nagumo (FHN)神经元系统的动力学性质,即稳态概率分布函数和其平均值. 给出了FHN神经元系统的稳态概率密度和平均值的解析表达式. 结果表明: 乘性噪声的自关联时间1、加性噪声的自关联时间2、加性噪声强度和乘性噪声强度D都能够诱导非平衡相变的产生. 和D的增大有利于系统从激发态向静息态转换. 1, 2的增大有利于系统从静息态向激发态转换. 噪声强度和其自关联时间的作用完全相反.

关键词:

Abstract

Making use of the unified colored noise approximation, the steady sate characteristics of the one-dimension of FitzHugh-Nagumo neural system with two different colored noises are investigated. The expressions of the steady state probability distribution function and the mean value are obtained. After numerical calculation, the results show that the self-correlated time of the multiplicative noise 1, the self-correlated time of the additive noise 2,the intensity of the additive noise , and the intensity of the multiplicative noise D can induce the transition. The increases of and D are conductive to the switch from the exciting state to the resting state. However, with 1 and 2 increasing, the switch from the resting state to the exciting state becomes obvious. The noise intensity and it self-correlated time play opposite roles.

Keywords:

FHN neural system /
colored noise /
steady state probability distribution function /
mean value

作者及机构信息

杨亚强¹,
王参军²

1.
宝鸡文理学院数学系, 宝鸡 721013;

2.
宝鸡文理学院非线性研究所, 宝鸡 721016

基金项目: 国家自然科学基金(批准号:11047146)、陕西省自然科学基金 (批准号:2010JQ1014)和宝鸡文理学院重点科研项目(批准号:ZK11053)资助的课题.

Authors and contacts

Yang Ya-Qiang¹,
Wang Can-Jun²

1.
Department of Mathematics, Baoji University of Arts and Sciences, Baoji 721013, China;

2.
Nonlinear Research Institute, Baoji University of Arts and Sciences, Baoji 721016, China

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11047146), the Natural Science Foundation of Shaanxi Province, China (Grant No.2010JQ1014), and the Science Foundation of Baoji University of Science and Arts, China (Grant No. ZK11053).

参考文献

[1]	Hu G 1994 Stochastic Forces and Nonlinear Systems (Shanghai: Shanghai scienti?c and Technological Education Press) (in Chinese) [胡岗 1994 随机力与非线性系统(上海:上海科技教育出版社)]
[2]	Moss F, McClintock P V E 1998 Noise in Nonlinear Dynamical Systems (Cambridge: Cambridge University Press) Vol.1--3
[3]	Liu Q, Jia Y 2004 Phys. Rev. E 70 041907
[4]	Wang C J, Mei D C 2008 Acta Phys. Sin. 57 3983 (in Chinese) [王参军, 梅冬成2008 物理学报 57 3983]
[5]	Wang C J 2012 Acta Phys. Sin. 61 010503 (in Chinese) [王参军 2012 物理学报 61 010503]
[6]	Braun H A, Wissing Schafer H K, Hirsch M C 1994 Nature 367 270
[7]	Ai B Q, Wang X J, Liu G T, Liu L G 2003 Phys. Rev. E 67 022903
[8]	Mei D C, Xie C W, Zhang L 2004 Eur. Phys. J. B 41 107
[9]	Wang C J, Wei Q, Mei D C 2008 Phys. Lett. A 372 2176
[10]	Wang C J, Wei Q, Zheng B B 2008 Acta Phys. Sin. 57 1735 (in Chinese) [王参军, 魏群, 郑宝兵2008 物理学报 57 1735]
[11]	Nie L R, Mei D C 2008 Phys. Rev. E 77 031107
[12]	Alarcón T, Pérez Madrid A, Rubí J M 1998 Phys. Rev. E 57 4979
[13]	Yu S N,Jia Y 2000 Journal of Central China Normal University (Nature Science) 34 281
[14]	Wang C Q, Xu W, Zhang N M, Li H Q 2008 Acta Phys. Sin. 57 749 (in Chinese) [王朝庆, 徐伟, 张娜敏, 李海泉 2008 物理学报 57 749]
[15]	Zhao Y, Xu W, Zou S C 2009 Acta Phys. Sin. 58 1396 (in Chinese) [赵燕, 徐伟, 邹少存 2009 物理学报 58 1396]
[16]	Cao L, Wu D J, Ke S Z 1995 Phys. Rev. E 52 3228
[17]	Sancho J M, San Miguel M, Katz S L and Gunton J D 1982 Phys. Rev. A 26 1589
[18]	Wang C J 2008 Chin. Phys. B 17 479

施引文献

[1]	Hu G 1994 Stochastic Forces and Nonlinear Systems (Shanghai: Shanghai scienti?c and Technological Education Press) (in Chinese) [胡岗 1994 随机力与非线性系统(上海:上海科技教育出版社)]
[2]	Moss F, McClintock P V E 1998 Noise in Nonlinear Dynamical Systems (Cambridge: Cambridge University Press) Vol.1--3
[3]	Liu Q, Jia Y 2004 Phys. Rev. E 70 041907
[4]	Wang C J, Mei D C 2008 Acta Phys. Sin. 57 3983 (in Chinese) [王参军, 梅冬成2008 物理学报 57 3983]
[5]	Wang C J 2012 Acta Phys. Sin. 61 010503 (in Chinese) [王参军 2012 物理学报 61 010503]
[6]	Braun H A, Wissing Schafer H K, Hirsch M C 1994 Nature 367 270
[7]	Ai B Q, Wang X J, Liu G T, Liu L G 2003 Phys. Rev. E 67 022903
[8]	Mei D C, Xie C W, Zhang L 2004 Eur. Phys. J. B 41 107
[9]	Wang C J, Wei Q, Mei D C 2008 Phys. Lett. A 372 2176
[10]	Wang C J, Wei Q, Zheng B B 2008 Acta Phys. Sin. 57 1735 (in Chinese) [王参军, 魏群, 郑宝兵2008 物理学报 57 1735]
[11]	Nie L R, Mei D C 2008 Phys. Rev. E 77 031107
[12]	Alarcón T, Pérez Madrid A, Rubí J M 1998 Phys. Rev. E 57 4979
[13]	Yu S N,Jia Y 2000 Journal of Central China Normal University (Nature Science) 34 281
[14]	Wang C Q, Xu W, Zhang N M, Li H Q 2008 Acta Phys. Sin. 57 749 (in Chinese) [王朝庆, 徐伟, 张娜敏, 李海泉 2008 物理学报 57 749]
[15]	Zhao Y, Xu W, Zou S C 2009 Acta Phys. Sin. 58 1396 (in Chinese) [赵燕, 徐伟, 邹少存 2009 物理学报 58 1396]
[16]	Cao L, Wu D J, Ke S Z 1995 Phys. Rev. E 52 3228
[17]	Sancho J M, San Miguel M, Katz S L and Gunton J D 1982 Phys. Rev. A 26 1589
[18]	Wang C J 2008 Chin. Phys. B 17 479

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