一类非线性神经网络中噪声改善信息传输

李欢; 王友国

doi:10.7498/aps.63.120506

摘要

以互信息为测度，通过数值计算和计算机仿真比较详细地讨论了在加性和乘性噪声共同作用下的一类非线性神经网络中噪声改善信息传输的（阈上）随机共振现象. 在一定的系统阈值和固定的乘性（或加性）噪声强度下，互信息随着加性（或乘性）噪声强度的增加显示出上凸变化，（阈上）随机共振出现；系统阈值单元数目的增加可增强信息传输的效果；系统阈值的增加使得信号处在阈下的成分增多，（阈上）随机共振现象更容易发生. 另外，改变加性噪声强度比改变乘性强度时（阈上）随机共振更容易发生. 以上结果说明（阈上）随机共振现象的存在性和噪声改善信息传输的效果与乘性或加性噪声强度、阈值单元数以及系统阈值水平密切相关.

关键词:

Abstract

In this paper, (supra-threshold) stochastic resonance phenomenon of noise-enhanced information transmission is studied in detail through the numerical calculation and the computer simulation in a non-linear multilevel threshold neural networks system, which is affected by both additive noise and multiplicative noise, then the mutual information is used to characterize the phenomenon. The mutual information as a function of additive noise intensity or multiplicative noise intensity brings on convex changes under a suitable system threshold and a fixed multiplicative noise intensity or additive noise intensity, which shows that the (supra-threshold) stochastic resonance phenomenon occurs. The increases in the number of the system threshold units can enhance the effectiveness of information transmission; the increase of the system threshold can increase the signal components that are under the threshold, and thus the supra-threshold stochastic resonance takes place more easily. In addition, by changing the additive noise intensity the supra-threshold stochastic resonance occurs more easily than by changing the multiplicative noise intensity. The above results show that both the existence of the supra-threshold stochastic resonance and the effectiveness of noise-improved the signal transmission are closely related to multiplicative or additive noise intensity, the number of threshold units, and the system threshold level.

Keywords:

neural networks system /
noises /
(supra-threshold) stochastic resonance /
mutual information

作者及机构信息

李欢,
王友国

1.
南京邮电大学理学院, 南京 210023

基金项目: 国家自然科学基金（批准号：61179027）资助的课题.

Authors and contacts

1.
College of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, China

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 61179027).

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施引文献

[1]	Benzi R, Stuera A, Vulpiani A 1981 J. Phys. A: Math. Gen. 14 L453
[2]
[3]	McNamara B, Wiesenfeld K 1998 Phys. Rev. A 39 4854
[4]	Gammaitoni L, Hanggi P, Jung P, Marchesoni F 1998 Rev. Mod. Phys. 70 223
[5]
[6]	Mitaim S, Kosko B 1998 Proc. IEEE 86 2152
[7]
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[9]	Chen H, Varshney P K, Kay S, Michels J H 2007 IEEE Trans. Sign. Process. 55 3172
[10]	Chapeau-Blondeau F, Godivier X 1997 Phys. Rev. E 55 1478
[11]
[12]	Fauve S, Heslot F 1983 Phys. Lett. A 97 5
[13]
[14]	McNamara B, Wiesenfeld K, Roy R 1988 Phys. Rev. Lett. 60 2626
[15]
[16]	Zhou T, Moss F, Jung P 1990 Phys. Rev. A 42 3161
[17]
[18]
[19]	Chialvo D R, Longtin A, Muller-Gerking J 1997 Phys. Rev. E 55 1798
[20]
[21]	Kay S 2000 IEEE Sign. Process. Lett. 7 8
[22]	Wang Y G, Wu L N 2007 Fluct. Noise Lett. 7 L449
[23]
[24]
[25]	Wang Y G, Wu L N 2005 Fluct. Noise Lett. 5 L435
[26]	Kosko B, Mitaim S 2003 Neural Networks 16 755
[27]
[28]
[29]	Bulsara A R, Zador A 1996 Phys. Rev. E 54 R2185
[30]	Guo F, Zhou Y R, Zhang Y 2010 Chin. Phys. B 19 070504
[31]
[32]	Collins J J, Chow C C, Capela A C, Imhoff T T 1995 Phys. Rev. E 52 3321
[33]
[34]	Stocks N G 2000 Phys. Rev. Lett. 84 2310
[35]
[36]	Nikitin A, Stocks N G, Morse R P 2007 Phys. Rev. E 75 021121
[37]
[38]	Cao J, Wang Z, Sun Y 2007 Physica A 385 718
[39]
[40]	Cao J, Daniel W C Ho, Huang X 2007 Nonlin. Anal. 66 1558
[41]
[42]	Stocks N G 2001 Phys. Rev. E 63 041114
[43]
[44]	Stocks N G, Mannella R 2001 Phys. Rev. E 64 030902
[45]
[46]
[47]	Mcdonnell M D, Stocks N G, Pearce C E M, Abbott D 2005 Fluct. Noise Lett. 5 L457
[48]	McDonnell M D, Abbott D, Pearce C E M 2002 Microelectr. J. 33 1079
[49]
[50]
[51]	Stocks N G, Allingham D, Morse R P 2002 Fluct. Noise Lett. 2 L169
[52]	Rousseau D, Duan F, Chapeau-Blondeau F 2003 Phys. Rev. E 68 031107
[53]
[54]
[55]	Rousseau D, Chapeau-Blondeau F 2004 Phys. Lett. A 321 280
[56]
[57]	Stocks N G 2001 Phys. Lett. A 279 308
[58]
[59]	Gammaitoni L, Marchesoni F, Menichella-Saetta E, Santucci S 1994 Phys. Rev. E 49 4878
[60]	Barzykin A V, Seki K 1997 Europhys. Lett. 40 117
[61]
[62]	Barzykin A V, Seki K, Shibata F 1998 Phys. Rev. E 57 6555
[63]
[64]
[65]	Zhang J J, Jin Y F 2012 Acta Phys. Sin. 61 130502 (in Chinese) [张静静, 靳艳飞 2012 61 130502]
[66]	Guo Y F, Tan J G 2012 Acta Phys. Sin. 61 170502 (in Chinese) [郭永峰, 谭建国 2012 61 170502]
[67]

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