System size stochastic resonance in asymmetric bistable coupled network systems

Sun Zhong-Kui; Lu Peng-Ju; Xu Wei

doi:10.7498/aps.63.220503

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

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.

References

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[16]	Sun Z K, Yang X L, Xiao Y Z, Xu W 2014 Chaos 24 023126
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[40]	Zhu X L, Zhang H T, Sang J P, Huang S Y, Zou X W 2014 Chin. Phys. B 23 068701
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[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]
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Cited By

[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 物理学报 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 物理学报 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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Vol. 63, Issue 22 - 2014-11-20

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