非对称双稳耦合网络系统的尺度随机共振研究

孙中奎; 鲁捧菊; 徐伟

doi:10.7498/aps.63.220503

摘要

研究了不同周期信号调制下非对称双稳耦合网络系统的尺度随机共振问题. 针对该网络系统, 首先运用高斯近似和役使原理对其进行了降维, 推导了其简化模型. 在绝热近似条件下, 利用Fokker-Planck方程分别得到了余弦信号和矩形信号调制下信噪比的解析表达式. 在此基础上, 研究了系统的尺度随机共振行为, 并讨论了非对称性、噪声强度、周期信号的振幅和耦合系数对系统尺度随机共振的影响. 结果表明, 两种情形下信噪比均是系统尺度的非单调函数, 说明在此网络系统中产生了共振现象.

关键词:

Abstract

In this paper, the noise-induced dynamics is studied in an asymmetric bistable coupled network system modulated by different signals. According to the Gaussian approximation and the slaving principle, the asymmetric bistable coupled network system is reduced to a low-dimensional model with two potentials, by which the phenomenon of system size stochastic resonance is studied theoretically and numerically. Under the assumption of adiabatic limit, the expressions of signal-to-noise ratio (SNR) are found by virtue of Fokker-Planck equation with respect to cosine signal and rectangle signal, based on which the system size stochastic resonance is investigated. Further, the effects of the noise strength, the asymmetry and the amplitude of the signal on the system size stochastic resonance are well discussed. It is demonstrated that the SNR shows a non-monotonic dependence on the number of coupled systems, which is demonstrated that there is a resonance with respect to the number of coupled systems.

Keywords:

system size stochastic resonance /
asymmetric bistable coupled network systems /
cosine signal /
rectangle signal

作者及机构信息

1.
西北工业大学应用数学系, 西安 710072

基金项目: 国家自然科学基金(批准号:11272258,11102156)和陕西省青年科技新星和西北工业大学基础研究基金资助的课题.

Authors and contacts

1.
Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11272258, 11102156), the Shaanxi Project for Young New Star in Science and Technology and the Northwestern Polytechnical University Foundation for Fundamental Research, China.

参考文献

[1]	Benzi R, Sutera A, Vulpiani A 1981 J. Phys. A: Math. Gen. 14 L453
[2]	Fauve S, Heslot F 1983 Phys. Lett. A 97 5
[3]	McNamara B, Wiesenfeld K, Roy R 1988 Phys. Rev. Lett. 60 2626
[4]	Julicher F, Ajdari A, Prost J 1997 Rev. Mod. Phys. 69 1269
[5]	Gammaitoni L, Hänggi P, Jung P, Marchesoni F 1998 Rev. Mod. Phys. 70 223
[6]	Li J H 2002 Phys. Rev. E 66 031104
[7]	Kang Y M, Xu J X, Xie Y 2003 Phys. Rev. E 68 036123
[8]	Wu D, Zhu S Q, Luo X Q, Wu L 2011 Phys. Rev. E 84 021102
[9]	Wang Q Y, Perc M, Duan Z S, Chen G R 2009 Phys. Rev. E 80 026206
[10]	Sun Z K, Yang X L, Xu W 2012 Phys. Rev. E 85 061125
[11]	Sun Z K, Yang X L 2011 Chaos 21 033114
[12]	Wu Y, Zhu W Q 2008 Phys. Rev. E 77 041911
[13]	Gan C B, Perc M, Wang Q Y 2010 Chin. Phys. B 19 040508
[14]	Liu L, Cao L, Zhang L 2010 Acta Phys. Sin. 59 1494 (in Chinese) [刘立, 曹力, 张莉 2010 59 1494]
[15]	Zhang X Y, Xu W, Zhou B C 2012 Acta Phys. Sin. 61 030501 (in Chinese) [张晓燕, 徐伟, 周丙常 2012 61 030501]
[16]	Sun Z K, Yang X L, Xiao Y Z, Xu W 2014 Chaos 24 023126
[17]	McNamara B, Wiesenfeld K 1989 Phys. Rev. A 39 4854
[18]	Gammaitoni L, Marchesoni F, Saetta M E, Santucci S 1989 Phys. Rev. Lett. 62 349
[19]	Zhou T, Moss F 1990 Phys. Rev. A 41 4255
[20]	Collins J J, Chow C C, Capela A C, Imhoff T T 1996 Phys. Rev. E 54 5575
[21]	Collins J J, Chow C C, Imhoff T T 1995 Phys. Rev. E 52 R3321
[22]	Heneghan C, Chow C C, Collins J J, Imhoff T T, Lowen S B, Teich M C 1996 Phys. Rev. E 54 R2228
[23]	Hu G, Gong D C, Wen X D, Yang C Y, Qing G R, Li R 1992 Phys. Rev. A 46 3250
[24]	Li J L, Xu B H 2006 Chin. Phys. 15 2867
[25]	Li J L 2007 Chin. Phys. 16 340
[26]	Grigorenko A N, Nikitin S I, Roschepkin G V 1997 Phys. Rev. E 56 R4907
[27]	Wiesenfeld K, Pierson D, Pantazelou E, Dames C, Moss F 1994 Phys. Rev. Lett. 72 2125
[28]	Pikovsky A S, Kurths J 1997 Phys. Rev. Lett. 78 775
[29]	Masoliver J, Robinson A, Weiss G H 1995 Phys. Rev. E 51 4021
[30]	Porra J M 1997 Phys. Rev. E 55 6533
[31]	Dhara A K, Mukhopadhyay T 1999 Phys. Rev. E 60 2727
[32]	Zhang Y, Hu G, Gammaitoni L 1998 Phys. Rev. E 58 2952
[33]	Krawiecki A 2004 Physica A 333 505
[34]	Bezrukov S M, Vodyanoy I 1995 Nature 378 362
[35]	Morse R P, Roper P 2000 Phys. Rev. E 61 5683
[36]	Xu H M, Wang Y 2003 Recent Developments in World Seismology 12 4 (in Chinese) [徐好民, 王煜 2003 国际地震动态 12 4]
[37]	Watt D J, Strogatz S H 1998 Nature 393 440
[38]	Strogatz S H 2001 Nature 410 268
[39]	Albert R, Barabasi A L 2002 Rev. Mod. Phys. 74 47
[40]	Zhu X L, Zhang H T, Sang J P, Huang S Y, Zou X W 2014 Chin. Phys. B 23 068701
[41]	Pikovsky A, Zaikin A, la de Casa M A 2002 Phys. Rev. Lett. 88 050601
[42]	Schmid G, Goychuk I, Hänggi P 2001 Europhys. Lett. 56 22
[43]	Schmid G, Goychuk I, Hänggi P 2004 Phys. Biol. 1 61
[44]	Toral R, Mirasso C R, Gunton J D 2003 Europhys. Lett. 61 162
[45]	Tessone C J, Toral R 2005 Physica A 351 106
[46]	Cubero D 2008 Phys. Rev. E 77 021112
[47]	Wu D J, Cao L, Chen L H 1990 Principles and Applications in Synergistics (Wuhan: Huazhong University of Science and Technology Press) pp67-93 (in Chinese) [吴大进, 曹力, 陈立华 1990 协同学原理和应用 (武汉: 华中理工大学出版社) 第67–93页]
[48]	Hu G 1991 Phys. Rev. A 43 700
[49]	Gerashchenko O V 2003 Tech. Phys. Lett. 29 256

施引文献

[1]	Benzi R, Sutera A, Vulpiani A 1981 J. Phys. A: Math. Gen. 14 L453
[2]	Fauve S, Heslot F 1983 Phys. Lett. A 97 5
[3]	McNamara B, Wiesenfeld K, Roy R 1988 Phys. Rev. Lett. 60 2626
[4]	Julicher F, Ajdari A, Prost J 1997 Rev. Mod. Phys. 69 1269
[5]	Gammaitoni L, Hänggi P, Jung P, Marchesoni F 1998 Rev. Mod. Phys. 70 223
[6]	Li J H 2002 Phys. Rev. E 66 031104
[7]	Kang Y M, Xu J X, Xie Y 2003 Phys. Rev. E 68 036123
[8]	Wu D, Zhu S Q, Luo X Q, Wu L 2011 Phys. Rev. E 84 021102
[9]	Wang Q Y, Perc M, Duan Z S, Chen G R 2009 Phys. Rev. E 80 026206
[10]	Sun Z K, Yang X L, Xu W 2012 Phys. Rev. E 85 061125
[11]	Sun Z K, Yang X L 2011 Chaos 21 033114
[12]	Wu Y, Zhu W Q 2008 Phys. Rev. E 77 041911
[13]	Gan C B, Perc M, Wang Q Y 2010 Chin. Phys. B 19 040508
[14]	Liu L, Cao L, Zhang L 2010 Acta Phys. Sin. 59 1494 (in Chinese) [刘立, 曹力, 张莉 2010 59 1494]
[15]	Zhang X Y, Xu W, Zhou B C 2012 Acta Phys. Sin. 61 030501 (in Chinese) [张晓燕, 徐伟, 周丙常 2012 61 030501]
[16]	Sun Z K, Yang X L, Xiao Y Z, Xu W 2014 Chaos 24 023126
[17]	McNamara B, Wiesenfeld K 1989 Phys. Rev. A 39 4854
[18]	Gammaitoni L, Marchesoni F, Saetta M E, Santucci S 1989 Phys. Rev. Lett. 62 349
[19]	Zhou T, Moss F 1990 Phys. Rev. A 41 4255
[20]	Collins J J, Chow C C, Capela A C, Imhoff T T 1996 Phys. Rev. E 54 5575
[21]	Collins J J, Chow C C, Imhoff T T 1995 Phys. Rev. E 52 R3321
[22]	Heneghan C, Chow C C, Collins J J, Imhoff T T, Lowen S B, Teich M C 1996 Phys. Rev. E 54 R2228
[23]	Hu G, Gong D C, Wen X D, Yang C Y, Qing G R, Li R 1992 Phys. Rev. A 46 3250
[24]	Li J L, Xu B H 2006 Chin. Phys. 15 2867
[25]	Li J L 2007 Chin. Phys. 16 340
[26]	Grigorenko A N, Nikitin S I, Roschepkin G V 1997 Phys. Rev. E 56 R4907
[27]	Wiesenfeld K, Pierson D, Pantazelou E, Dames C, Moss F 1994 Phys. Rev. Lett. 72 2125
[28]	Pikovsky A S, Kurths J 1997 Phys. Rev. Lett. 78 775
[29]	Masoliver J, Robinson A, Weiss G H 1995 Phys. Rev. E 51 4021
[30]	Porra J M 1997 Phys. Rev. E 55 6533
[31]	Dhara A K, Mukhopadhyay T 1999 Phys. Rev. E 60 2727
[32]	Zhang Y, Hu G, Gammaitoni L 1998 Phys. Rev. E 58 2952
[33]	Krawiecki A 2004 Physica A 333 505
[34]	Bezrukov S M, Vodyanoy I 1995 Nature 378 362
[35]	Morse R P, Roper P 2000 Phys. Rev. E 61 5683
[36]	Xu H M, Wang Y 2003 Recent Developments in World Seismology 12 4 (in Chinese) [徐好民, 王煜 2003 国际地震动态 12 4]
[37]	Watt D J, Strogatz S H 1998 Nature 393 440
[38]	Strogatz S H 2001 Nature 410 268
[39]	Albert R, Barabasi A L 2002 Rev. Mod. Phys. 74 47
[40]	Zhu X L, Zhang H T, Sang J P, Huang S Y, Zou X W 2014 Chin. Phys. B 23 068701
[41]	Pikovsky A, Zaikin A, la de Casa M A 2002 Phys. Rev. Lett. 88 050601
[42]	Schmid G, Goychuk I, Hänggi P 2001 Europhys. Lett. 56 22
[43]	Schmid G, Goychuk I, Hänggi P 2004 Phys. Biol. 1 61
[44]	Toral R, Mirasso C R, Gunton J D 2003 Europhys. Lett. 61 162
[45]	Tessone C J, Toral R 2005 Physica A 351 106
[46]	Cubero D 2008 Phys. Rev. E 77 021112
[47]	Wu D J, Cao L, Chen L H 1990 Principles and Applications in Synergistics (Wuhan: Huazhong University of Science and Technology Press) pp67-93 (in Chinese) [吴大进, 曹力, 陈立华 1990 协同学原理和应用 (武汉: 华中理工大学出版社) 第67–93页]
[48]	Hu G 1991 Phys. Rev. A 43 700
[49]	Gerashchenko O V 2003 Tech. Phys. Lett. 29 256

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