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

关联高斯与非高斯噪声激励的FHN神经元系统的稳态分析

申雅君 郭永峰 袭蓓

引用本文:
Citation:

关联高斯与非高斯噪声激励的FHN神经元系统的稳态分析

申雅君, 郭永峰, 袭蓓

Steady state characteristics in FHN neural system driven by correlated non-Gaussian noise and Gaussian noise

Shen Ya-Jun, Guo Yong-Feng, Xi Bei
PDF
导出引用
  • 本文主要研究了关联乘性非高斯噪声和加性高斯白噪声共同激励的FHN (FitzHugh-Nagumo) 神经元系统. 利用路径积分法和统一色噪声近似, 推导出该系统的定态概率密度函数表达式. 通过研究发现, 乘性噪声强度D、加性噪声强度Q、噪声自关联时间 以及互关联系数 均可以诱导系统产生非平衡相变现象, 而非高斯参数q却不可以诱导系统产生非平衡相变现象. 此外, 我们还发现参数D和 的增大有利于神经元系统从激发态向静息态转换,Q和 的增大有利于神经元系统从静息态向激发态转换, q的增大会使得神经元系统停留在静息态的概率增加.
    Recently, the dynamics problems of nonlinear systems driven by noises have attracted considerable attention. The researches indicate that the noise plays a determinative role in system evolution. This irregular random interference does not always play a negative role in the macro order. Sometimes it can play a positive role. The various effects of noise are found in physics, biology, chemistry and other fields, such as noise-induced non-equilibrium phase transition, noise-enhanced system stability, stochastic resonance, etc. Especially, in the field of biology, the effects of noise on life process are significant. At present, a large number of researchers have studied the kinetic properties of the neuron system subjected to noises. However, these studies focus on the Gaussian noise, while the researches about non-Gaussian noise are less. In fact, it is found that all the noise sources among neuronal systems, physical systems and biological systems tend to non-Gaussian distribution. So it is reasonable to consider the effects of the non-Gaussian noise on systems, and it is closer to the actual process. Therefore, it has some practical significance to study the FHN system driven by the non-Gaussian noise and analyze the kinetic properties of this system. In this work, we study the stationary probability distribution (SPD) in FitzHugh-Nagumo (FHN) neural system driven by correlated multiplicative non-Gaussian noise and additive Gaussian white noise. Using the path integral approach and the unified colored approximation, the analytical expression of the stationary probability distribution is first derived, and then the change regulations of the SPD with the strength and relevance between multiplicative noise and additive noise are analyzed. After that, the simulation results show that the intensity of multiplicative noise, the intensity of additive noise, the correlation time of the non-Gaussian noise and the cross-correlation strength between noises can induce non-equilibrium phase transition. This means that the effect of the non-Gaussian noise intensity on SPD is the same as that of the Gaussian noise intensity. However, the non-Gaussian noise deviation parameter cannot induce non-equilibrium phase transition. Moreover, we also find that the increases of the multiplicative noise intensity and the cross-correlation strength between noises are conducive to the conversion of the exciting state into the resting state. And with the additive noise intensity and the correlation time increasing, the conversion of the resting state into the exciting state becomes obvious. Meanwhile, the increase of non-Gaussian noise deviation parameter increases the probability of staying in the resting state.
      通信作者: 郭永峰, guoyongfeng@mail.nwpu.edu.cn
    • 基金项目: 国家自然科学基金(批准号: 11102132)资助的课题.
      Corresponding author: Guo Yong-Feng, guoyongfeng@mail.nwpu.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11102132).
    [1]

    Mangioni S, Deza R 2000 Phys. Rev. E 61 223

    [2]

    Van den Broeck C, Parrondo J M R, Toral R 1994 Phys. Rev. Lett. 73 3395

    [3]

    Hnggi P, Jung P, Zerbe C, Moss F 1993 J. Stat. Phys. 70 25

    [4]

    He M J, Xu W, Sun Z K, Du L 2015 Commun. Nonlinear Sci. Numer. Simul. 28 39

    [5]

    Sun Z K, Yang X L, Xu W 2012 Phys. Rev. E 85 061125

    [6]

    Sun Z K, Yang X L, Xiao Y Z, Xu W 2014 Chaos 24 023126

    [7]

    Sun Z K, Wu Y Z, Du L, Xu W 2016 Nonlinear Dyn. 84 1011

    [8]

    Sun Z K, Yang X L 2011 Chaos 21 033114

    [9]

    Sun Z K, Fu J, Xiao Y Z, Xu W 2015 Chaos 25 083102

    [10]

    Sun Z K, Yang X L, Xu W 2016 Sci. China Technol. Sci. 59 403

    [11]

    Yang X L, Senthilkumar D V, Sun Z K, Kurths J 2011 Chaos 21 047522

    [12]

    Sun Z K, Lu P J, Xu W 2014 Acta Phys. Sin. 63 220503 (in Chinese) [孙中奎, 鲁捧菊, 徐伟 2014 物理学报 63 220503]

    [13]

    Bezrnkov S M, Vodyanoy I 1997 Nature 385 319

    [14]

    Goychuk I, Hnggi P 2000 Phys. Rev. E 61 4272

    [15]

    Hodgkin A L, Huxley A F 1952 Physiology 117 500

    [16]

    Wiesenfeld K, Pierson D, Pantazelou E, Dames C, Moss F 1994 Phys. Rev. Lett 72 2125

    [17]

    Tuckwell H C, Rodriguez R, Wan F Y M 2003 Neural Comput. 15 143159

    [18]

    Acebron J A, Bulsara A R, Rappel W J 2004 Phys. Rev. E 69 026202

    [19]

    Kitajima H, Kurths J 2005 Chaos 15 023704

    [20]

    Fitzhhugh R 1960 J. Gen. Physiol. 43 867

    [21]

    Alarcon T, Perez-Madrid A, Rubi J M 1998 Phys. Rev. E 57 4979

    [22]

    Wang Z Q, Xu Y, Yang H 2016 Sci. China: Technol. Sci. 59 371

    [23]

    Xiao Y Z, Tang S F, Sun Z K 2014 Eur. Phys. J. B 87 134

    [24]

    Zhang J J, Jin Y F 2012 Acta Phys. Sin. 61 130502 (in Chinese) [张静静, 靳艳飞 2012 物理学报 61 130502]

    [25]

    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]

    [26]

    Gardiner C W 1985 Handbook of Stochastic Methods (Berlin: Springer-Verlag) pp80-115

    [27]

    Bouzat S, Wio H S 2005 Physica A 351 69

    [28]

    Fuentes M A, Wio H S, Toral R 2002 Physica A 303 91

    [29]

    Wio H S, Colet P, San Miguel M, Pesquera L, Rodrguez M A 1989 Phys. Rev. A 40 7312

    [30]

    Wu D, Zhu S Q 2007 Phys. Lett. A 363 202

    [31]

    Jung P, Hnggi P 1987 Phys. Rev. A 35 4464

    [32]

    Cao L, Wu D J, Ke S Z 1995 Phys. Rev. E 52 3228

  • [1]

    Mangioni S, Deza R 2000 Phys. Rev. E 61 223

    [2]

    Van den Broeck C, Parrondo J M R, Toral R 1994 Phys. Rev. Lett. 73 3395

    [3]

    Hnggi P, Jung P, Zerbe C, Moss F 1993 J. Stat. Phys. 70 25

    [4]

    He M J, Xu W, Sun Z K, Du L 2015 Commun. Nonlinear Sci. Numer. Simul. 28 39

    [5]

    Sun Z K, Yang X L, Xu W 2012 Phys. Rev. E 85 061125

    [6]

    Sun Z K, Yang X L, Xiao Y Z, Xu W 2014 Chaos 24 023126

    [7]

    Sun Z K, Wu Y Z, Du L, Xu W 2016 Nonlinear Dyn. 84 1011

    [8]

    Sun Z K, Yang X L 2011 Chaos 21 033114

    [9]

    Sun Z K, Fu J, Xiao Y Z, Xu W 2015 Chaos 25 083102

    [10]

    Sun Z K, Yang X L, Xu W 2016 Sci. China Technol. Sci. 59 403

    [11]

    Yang X L, Senthilkumar D V, Sun Z K, Kurths J 2011 Chaos 21 047522

    [12]

    Sun Z K, Lu P J, Xu W 2014 Acta Phys. Sin. 63 220503 (in Chinese) [孙中奎, 鲁捧菊, 徐伟 2014 物理学报 63 220503]

    [13]

    Bezrnkov S M, Vodyanoy I 1997 Nature 385 319

    [14]

    Goychuk I, Hnggi P 2000 Phys. Rev. E 61 4272

    [15]

    Hodgkin A L, Huxley A F 1952 Physiology 117 500

    [16]

    Wiesenfeld K, Pierson D, Pantazelou E, Dames C, Moss F 1994 Phys. Rev. Lett 72 2125

    [17]

    Tuckwell H C, Rodriguez R, Wan F Y M 2003 Neural Comput. 15 143159

    [18]

    Acebron J A, Bulsara A R, Rappel W J 2004 Phys. Rev. E 69 026202

    [19]

    Kitajima H, Kurths J 2005 Chaos 15 023704

    [20]

    Fitzhhugh R 1960 J. Gen. Physiol. 43 867

    [21]

    Alarcon T, Perez-Madrid A, Rubi J M 1998 Phys. Rev. E 57 4979

    [22]

    Wang Z Q, Xu Y, Yang H 2016 Sci. China: Technol. Sci. 59 371

    [23]

    Xiao Y Z, Tang S F, Sun Z K 2014 Eur. Phys. J. B 87 134

    [24]

    Zhang J J, Jin Y F 2012 Acta Phys. Sin. 61 130502 (in Chinese) [张静静, 靳艳飞 2012 物理学报 61 130502]

    [25]

    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]

    [26]

    Gardiner C W 1985 Handbook of Stochastic Methods (Berlin: Springer-Verlag) pp80-115

    [27]

    Bouzat S, Wio H S 2005 Physica A 351 69

    [28]

    Fuentes M A, Wio H S, Toral R 2002 Physica A 303 91

    [29]

    Wio H S, Colet P, San Miguel M, Pesquera L, Rodrguez M A 1989 Phys. Rev. A 40 7312

    [30]

    Wu D, Zhu S Q 2007 Phys. Lett. A 363 202

    [31]

    Jung P, Hnggi P 1987 Phys. Rev. A 35 4464

    [32]

    Cao L, Wu D J, Ke S Z 1995 Phys. Rev. E 52 3228

  • [1] 杨棣, 王元美, 李军刚. 贝叶斯频率估计中频率的先验分布对有色噪声作用的影响. 物理学报, 2018, 67(6): 060301. doi: 10.7498/aps.67.20171911
    [2] 刘瑞芬, 惠治鑫, 熊科诏, 曾春华. 表面催化反应模型中关联噪声诱导非平衡相变. 物理学报, 2018, 67(16): 160501. doi: 10.7498/aps.67.20180250
    [3] 杨恒占, 钱富才, 高韵, 谢国. 随机系统的概率密度函数形状调节. 物理学报, 2014, 63(24): 240508. doi: 10.7498/aps.63.240508
    [4] 杨波, 梅冬成. 非高斯噪声对惯性棘轮中粒子负迁移率的影响. 物理学报, 2013, 62(11): 110502. doi: 10.7498/aps.62.110502
    [5] 靳晓琴, 许勇, 张慧清. 非高斯噪声驱动下一维双稳系统的逻辑操作. 物理学报, 2013, 62(19): 190510. doi: 10.7498/aps.62.190510
    [6] 何亮, 杜磊, 黄晓君, 陈华, 陈文豪, 孙鹏, 韩亮. 金属互连电迁移噪声的非高斯性模型研究. 物理学报, 2012, 61(20): 206601. doi: 10.7498/aps.61.206601
    [7] 杨亚强, 王参军. 双色噪声激励下FHN神经元系统的稳态性质. 物理学报, 2012, 61(12): 120507. doi: 10.7498/aps.61.120507
    [8] 张静静, 靳艳飞. 非高斯噪声激励下FitzHugh-Nagumo神经元系统的随机共振. 物理学报, 2012, 61(13): 130502. doi: 10.7498/aps.61.130502
    [9] 顾仁财, 许勇, 张慧清, 孙中奎. 非高斯Lvy噪声驱动下的非对称双稳系统的相转移和平均首次穿越时间. 物理学报, 2011, 60(11): 110514. doi: 10.7498/aps.60.110514
    [10] 张静静, 靳艳飞. 非高斯噪声驱动下非对称双稳系统的平均首次穿越时间与随机共振研究. 物理学报, 2011, 60(12): 120501. doi: 10.7498/aps.60.120501
    [11] 徐超, 康艳梅. 非高斯噪声激励下含周期信号FitzHugh-Nagumo系统的响应特征. 物理学报, 2011, 60(10): 108701. doi: 10.7498/aps.60.108701
    [12] 郭培荣, 徐伟, 刘迪. 非高斯噪声驱动的双奇异随机系统的熵流与熵产生. 物理学报, 2009, 58(8): 5179-5185. doi: 10.7498/aps.58.5179
    [13] 赵燕, 徐伟, 邹少存. 非高斯噪声激励下FHN神经元系统的定态概率密度与平均首次穿越时间. 物理学报, 2009, 58(3): 1396-1402. doi: 10.7498/aps.58.1396
    [14] 郭永峰, 徐 伟. 关联白噪声驱动的具有时间延迟的Logistic系统. 物理学报, 2008, 57(10): 6081-6085. doi: 10.7498/aps.57.6081
    [15] 王朝庆, 徐 伟, 张娜敏, 李海泉. 色噪声激励下的FHN神经元系统. 物理学报, 2008, 57(2): 749-755. doi: 10.7498/aps.57.749
    [16] 邵元智, 钟伟荣, 卢华权, 雷石付. Ising自旋体系的非平衡动态相变. 物理学报, 2006, 55(4): 2057-2063. doi: 10.7498/aps.55.2057
    [17] 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
    [18] 闫桂沈, 李贺军, 郝志彪. 热解碳化学气相沉积中的多重定态和非平衡相变的研究. 物理学报, 2002, 51(2): 326-331. doi: 10.7498/aps.51.326
    [19] 常胜江, 刘, 张文伟, 申金媛, 翟宏琛, 张延. 适用于神经元状态非等概率分布的神经网络模型及其光学实现. 物理学报, 1998, 47(7): 1101-1109. doi: 10.7498/aps.47.1101
    [20] 周光召, 苏肇冰. 非平衡耗散系统定常态的Goldstone模. 物理学报, 1980, 29(5): 618-634. doi: 10.7498/aps.29.618
计量
  • 文章访问数:  3411
  • PDF下载量:  264
  • 被引次数: 0
出版历程
  • 收稿日期:  2016-03-08
  • 修回日期:  2016-04-09
  • 刊出日期:  2016-06-05

关联高斯与非高斯噪声激励的FHN神经元系统的稳态分析

    基金项目: 国家自然科学基金(批准号: 11102132)资助的课题.

摘要: 本文主要研究了关联乘性非高斯噪声和加性高斯白噪声共同激励的FHN (FitzHugh-Nagumo) 神经元系统. 利用路径积分法和统一色噪声近似, 推导出该系统的定态概率密度函数表达式. 通过研究发现, 乘性噪声强度D、加性噪声强度Q、噪声自关联时间 以及互关联系数 均可以诱导系统产生非平衡相变现象, 而非高斯参数q却不可以诱导系统产生非平衡相变现象. 此外, 我们还发现参数D和 的增大有利于神经元系统从激发态向静息态转换,Q和 的增大有利于神经元系统从静息态向激发态转换, q的增大会使得神经元系统停留在静息态的概率增加.

English Abstract

参考文献 (32)

目录

    /

    返回文章
    返回