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

[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

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

[1]	Wang Ye-Hua, He Mei-Juan. Stochastic resonance in asymmetric bistable coupled network systems driven by Gaussian colored noise. Acta Physica Sinica, 2022, 71(19): 190501. doi: 10.7498/aps.71.20220909
[2]	Jiao Shang-Bin, Yang Rong, Zhang Qing, Xie Guo. Stochastic resonance of asymmetric bistable system with α stable noise. Acta Physica Sinica, 2015, 64(2): 020502. doi: 10.7498/aps.64.020502
[3]	Huang Xiang-Dong, Ding Dao-Xian, Nan Nan, Wang Zhao-Hua. Frequency estimation of undersampled sinusoidal signal based on chinese remainder theorem. Acta Physica Sinica, 2014, 63(19): 198403. doi: 10.7498/aps.63.198403
[4]	Peng Hao, Zhong Su-Chuan, Tu Zhe, Ma Hong. Stochastic resonance of over-damped bistable system driven by chirp signal and Gaussian white noise. Acta Physica Sinica, 2013, 62(8): 080501. doi: 10.7498/aps.62.080501
[5]	Gao Shi-Long, Zhong Su-Chuan, Wei Kun, Ma Hong. Weak signal detection based on chaos and stochastic resonance. Acta Physica Sinica, 2012, 61(18): 180501. doi: 10.7498/aps.61.180501
[6]	Zhang Li, Yuan Xiu-Hua, Wu Li. Stochastic resonance for pulse signal modulated by noise in a single-mode laser system. Acta Physica Sinica, 2012, 61(11): 110501. doi: 10.7498/aps.61.110501
[7]	Yang Ding-Xin, Hu Zheng, Yang Yong-Min. The analysis of stochastic resonance of periodic signal with large parameters. Acta Physica Sinica, 2012, 61(8): 080501. doi: 10.7498/aps.61.080501
[8]	Zhang Xiao-Yan, Xu Wei, Zhou Bing-Chang. Stochastic resonance in a time-delayed asymmetric mono-stable system modulated by periodic rectangular signal. Acta Physica Sinica, 2012, 61(3): 030501. doi: 10.7498/aps.61.030501
[9]	Lu Zhi-Xin, Cao Li. Stochastic resonance of square wave signal in an overdamped harmonic oscillator. Acta Physica Sinica, 2011, 60(11): 110501. doi: 10.7498/aps.60.110501
[10]	Zhu Guang-Qi, Ding Ke, Zhang Yu, Zhao Yuan. Experimental research of weak signal detection based on the stochastic resonance of nonlinear system. Acta Physica Sinica, 2010, 59(5): 3001-3006. doi: 10.7498/aps.59.3001
[11]	Ning Li-Juan, Xu Wei. Stochastic resonance under modulated noise in linear systems driven by dichotomous noise. Acta Physica Sinica, 2009, 58(5): 2889-2894. doi: 10.7498/aps.58.2889
[12]	Zhang Liang-Ying, Jin Guo-Xiang, Cao Li. Stochastic resonance of frequency modulated signals in a linear model of single-mode laser. Acta Physica Sinica, 2008, 57(8): 4706-4711. doi: 10.7498/aps.57.4706
[13]	Lin Min, Huang Yong-Mei, Fang Li-Min. The stochastic resonance control of coupled bistable systems. Acta Physica Sinica, 2008, 57(4): 2048-2052. doi: 10.7498/aps.57.2048
[14]	Zhou Bing-Chang, Xu Wei. Stochastic resonance in an asymmetric bistable system driven by correlated noise. Acta Physica Sinica, 2008, 57(4): 2035-2040. doi: 10.7498/aps.57.2035
[15]	Lin Min, Fang Li-Min, Zhu Ruo-Gu. The dual-resonance characteristic of coupled bistable system affected by two-frequency signal. Acta Physica Sinica, 2008, 57(5): 2638-2642. doi: 10.7498/aps.57.2638
[16]	Dong Xiao-Juan. Stochastic resonance in an asymmetric bistable system with time-delayed feedback and correlated noises. Acta Physica Sinica, 2007, 56(10): 5618-5622. doi: 10.7498/aps.56.5618
[17]	Zhou Bing-Chang, Xu Wei. Stochastic resonance in an asymmetric bistable system driven by mixed periodic force and noises. Acta Physica Sinica, 2007, 56(10): 5623-5628. doi: 10.7498/aps.56.5623
[18]	Jin Yan-Fei, Xu Wei, Li Wei, Xu Meng. Stochastic resonance for periodically modulated noise in a linear system. Acta Physica Sinica, 2005, 54(6): 2562-2567. doi: 10.7498/aps.54.2562
[19]	Xu Wei, Jin Yan-Fei, Xu Meng, Li Wei. Stochastic resonance for bias-signal-modulated noise in a linear system. Acta Physica Sinica, 2005, 54(11): 5027-5033. doi: 10.7498/aps.54.5027
[20]	Zhang Jia-Shu, Li Heng-Chao, Xiao Xian-Ci. A DCT domain quadratic predictor for real-time prediction of continuous chaotic signals. Acta Physica Sinica, 2004, 53(3): 710-716. doi: 10.7498/aps.53.710

Catalog

Vol. 63, Issue 22 - 2014-11-20

Metrics

Abstract views: 4953
PDF Downloads: 396
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板